Offhand I believe that Court de Gébelin was the first to suggest it.
Ménestrier believed cards to be a French invention (1392), and Tarot a German one. No place for Gypsy theories.
The next writer on playing cards, Gabriel (Father) Daniel, 1720, has heard speculations that cards were known to the Greeks and Romans, but believes them to have been in France only since the 14th century -
Origine du jeu du Piquet, trouvée dans l’Histoire de France
(Memoires pour l’histoire des Sciences & des beaux Arts (Trevoux, May 1720) Article XLII (pp. 934-968))
While reading attentively the History of France, reflections present themselves to the mind on subjects which seem to have no relation with it, but which however, by the combination of certain circumstances, are found to have much. Who would be inclined to think that the game of Piquet shows us one of the most famous reigns of our History; I mean to say that of Charles VII; that the economy of this game, the division of the cards, the different figures depicted on the cards, the manner in which it is played, instruct us with the most wonderful maxims of the State and of war, whose violation had caused all the problems of the Kingdom, in the first years of the Reign of this Prince, as well as during the greater part of that of his predecessor Charles VI, and the observation of which during the later years of the Reign of Charles VII had produced the reestablishment of France, and carried the glory of the Kingdom and the Sovereign as high as they could reach? It is this that I attempting to make clear, or at least very plausible, in this type of dissertation.
In it, I try to show firstly that this game was born in France; secondly, that it was invented during the Reign of Charles VII; thirdly, that this game is symbolic and that it contains a number of instructions for government and war; fourthly, that it makes continual allusion to various circumstances in which Charles VII found himself during his Reign.
I am not examining here whether certain card games which had some resemblance to those of our time were in use among the Greeks and Romans. I keep myself in France, and I say that card games have not been in use for more than four hundred years in the Kingdom; this Era seems to me to have been well proven by Father Menestrier in his Bibliothèque Curieuse.
He demonstrates this by an Ordonnance of King Charles VI, of the year 1391, in which this Prince enumerated the games with which his subjects were then occupied, to the neglect of those which would dispose them to military exercises; he prohibits them under penalty of a fine.
The games of which he speaks in the Ordonnance are the game of dice, the game of checkers, the game of billiards, etc., and he nowhere mentions that of cards, which doubtless, because of the rationale of the Ordonnance, would have been one of the first mentioned, if it had been then in use.
The same Author at the same time places the timing of this game, which was in the year after this Ordonnance, in 1392, and the occasion of its invention. This was the same year that Charles VI went mad, and when the Court applied itself to disperse his melancholy by all kinds of means. On this subject, he cites an account of Charles Poupart, King’s Treasurer, where it is said: to Jacquemin Gringonneur, Painter, for three packs of cards in gold and in different colors, of many signs, to take to the said Lord (King), for his amusement, LVI Parisian sols.
Father Menestrier adds, to confirm his impression, that one sees neither bas-reliefs, nor paintings, nor tapestries before this time where this game is shown, whereas one sees in many of them dice, checkerboards, dicing cups, etc., and that finally our old Romances often of all these games without making the slightest mention of card games, from which he concludes that the game of cards were in no way introduced into France before the Reign of Charles VI. As for the game of Piquet in particular, he does not pinpoint the time, and it is this that we are looking for.
Beneton de Peyrins, 1738, is fairly modern in his theory - China, Middle East, Moors in Spain; but although he also thinks late antique Rome knew playing cards, he doesn't invoke Gypsies to explain their presence -
Dissertation on the origin of games of chance, by Beneton de Peyrins
(published originally in the Mercure of September, 1738; it was reprinted by Leber in Collection des meilleurs dissertations, notices et traités particuliers relatifs a l'histoire de France (Paris 1838) tome X, pp. 201-219)
It has been seen above that all games of chance are expressed the generic term alea; and presently whoever would like to express in Latin the games that operate by means of cards, can only do so by those of folium lusorium aleatorium, which may open the door to the suspicion that the use of these cards is more ancient than hitherto believed, and that they could even have the same antiquity of origin of the dice and knuckle-bones used in other games called lusorium aleatorium. As for me, my sentiment is that cards were known during the decline of the Roman empire, that it was the conquests that had pushed well before into India, which allowed the cards invented by the Chinese to be carried into Syria and Egypt, where they were made with the paper of this latter country, consisting of the plant papyrus; and although that which I am advancing cannot be supported by passages of authors of this time, this silence can be attributed to the paucity of writers who appear in the decline of the Roman empire, and even to the disruption of this empire, which caused the knowledge of many new discoveries which existed during this disruption to be lost. The nations of the north which caused it, being ashamed of their ignorance and barbarity, in order to render these faults less noticeable, seemed to apply themselves to the task of destroying everything that could show a superior genius to theirs, which those they had submitted to had had. This is why these invasions, which caused the almost total loss of sciences and arts, also caused the loss of games of chance; and since it is certain that this was there the cause which made Europe forget the games of Chess and Trictrac, which afterwards came to us again from Asia, that was equally what was able to cause the loss of the memory that cards had been known in Rome.
The Asiatics, who were the first to know cards, distinguished them, in the way we still do, between simple or plain, and figures; on the figures there appeared the pictures of their gods and their heroes, and on the plain, there only appeared hieroglyphic characters, which served in the past as writing. These are the same characters which still mark our plain cards up to the present: the Chinese had, in hieroglyphs proper to express their thoughts, figures of hearts, pikes, tiles and flowers somewhat similar to clovers. The changes that time would bring to these figures is a little thing. The Romans preserved these plain cards in their own figures, and to the court cards they joined others bearing portraits of some of their principal gods, emperors and empresses, making them appear in triumphal chariots, from which come the terms triomphe, imperial and vole, in common use in playing cards as the names of two ancient games, and to express the complete victory that one can achieve with these cards, in imitation of these total victories that submitted an entire nation to the Romans, and made the general who achieved them deserve the triumph.
It must not be doubted that the Saracens and Greeks of the Late Empire knew card games, but they used them less than Chess and dice. We owe to the Moors who conquered Spain the game of Ombre; they fixed the suits visible on the cards, which are two reds and two blacks, in imitation of the colours by which they distinguished themselves in combat, divided into quadrilles in the gallant tournaments which they held in the honour of ladies; and the French who travelled in the East and in Spain since the twelfth century, recounted the knowledge of these cards and the games they played with them. But because, up to the time of Charles VI, they were too busy, as much with foreign wars as those arising within the country, besides the fact that games for the exercise of the body, such as tournaments, carrousels, and military and gallant parades amused them enough, when some interval of peace gave them the leisure to dream of diversions; and as it is only to the extent that the taste for exercises is lost, that that for games of chance increases, one must thus go down to the reign of Charles VI, and even later, to see the use of cards become well-established. It was then that they were given their form, and that they were placed in the arrangement that they have. For this, the characters or markings which are seen on the plain cards began to multiply, which was judged necessary, in order to give them different values, and, thereby, to make them useful to more kinds of games. As for the figured cards, the figures of the gods of paganism which may have remained were removed; and nevertheless, in order to preserve by means of figures which ones it was resolved to put there, the memory that these cards had been in use among all the most famous nations, the portraits of the greatest Kings and Captains were depicted, and the most illustrious Queens or women who had appeared in these nations; it is because of this that there are seen the David, Rachel, Esther and Judith of the Hebrews; the Pallas and Hector of Troy; the Alexander of the Greeks; the Caesar of the Romans; the Charlemagne of the French and Germans; the Argine of the English; the Ogier of the Danes; and for Potou and la Hire, these are two brave French captains who lived at the time when the arrangement of which I speak was given to the cards.
Bullet, 1757, adds the notion that cards need paper, and that since in Europe paper is unknown before the 12th century, cards can't have been invented before this time -
"I should add that cardboard, and consequently cards, could not have been invented before rag-paper, which we ourselves use today, was known in Europe; and the usage of this paper among us cannot be placed earlier than the twelfth century : cards therefore cannot be placed earlier than this time."
Recherches historiques sur les cartes à jouer (Lyon, J. Deville, 1757)
He follows Ménestrier in thinking that cards are a European invention. No place for Gypsies to have carried them around.
Finally the Abbé Rive, 1780, after dismissing previous authors' claims for France, Italy and Germany (let alone ancient Lydia), places the invention of cards in Spain in the 14th century. Court de Gébelin follows this, but since he believe cards to have come from Tarot, and Tarot from Egypt, he attributes the survival of Tarot, and therefore the original playing cards, to the (E)Gyp(t)sies.
I don't think Gypsies would have played a role in any other theory before Court de Gébelin,
a priori.