The Café de la Régence where Morphy gave his famous blindfold exhibition in 1858 was not the same Régence of Philidor and Bourdonnais. It too had been renovated and relocated.

In 1852 the Café de la Régence lost its original home on Place du Palais-Royal, where it opened in 1681 as one of the first coffee houses in Paris. It found temporary quarters on Rue de Richelieu for two years, then moved permanently to the Rue Saint-Honoré, where it remains to this day, though under a different name. The removal of the Café from its time honored location symbolized its removal from the history of chess. When the immortal American master Morphy gave a fantastic exhibition in the Café's new home in the late 1850's, playing eight blindfold games simultaneously, it was the visit of Morpheus, and the Café de la Régence has slept peacefully ever since.
     -Paul Metzner, Crescendo of the Virtuoso,  p.53
 

from a cleaned-up machine translation:

Located formerly at the corner of the street Saint-Honoré and the place of the Palais Royal, this establishment had famous customers and chess players of a remarkable strength. These included Deschapelles, Bourdonnais, Philidor, Saint-Amant,  General Bonaparte (this last was not a particularly great chess player). Alfred de Musset was, until incapacitated by his disease [Musset's Disease - an ailment of the heart brought on by heavy drinking], one of faithful of la Régence. He was a strong player. Knowing the habits of this famous author of the tales of Spain and Italy [more famous as a French poet], people from  foreign lands, as well as from the provinces, ones came to the Cafés just to watch him play.

...

On the long terrace in edge on the place of the Théâtre Français , one sees only foreigners, English, Americans. Scandinavians, Germans. The Norwegians, the Swedes, the Danes are there as on their own premises. The newspapers are received: from Stockholm, Copenhagen and Christiana, and the compatriots of Mrs. Nilsson devote themselves to literary or political discussions in this language that very little of French include/understand.

Having crossed  so noisy a terrace, one can enter a small room where the chess players sit at their tables. There, no sharp discussions, not even a movement. One only hears the small sharp snap of a chess piece as someone makes a manœuvrer. Formerly one did not smoke in this room; but the love of the tobacco grew popular even with the chess amateurs; the cigarettes, cigars and even pipes form clouds of smoke there at times. The chess players are so absorbed, that very often forget to eat that which they paid for; sometimes forget to drink the grog that they ordered or, as they never look at anything other than the battle field, – i.e. the board where they deploy their skill – if they drink, they sometimes accidentally drink their opponent's order, swallowing a coffee or beer mouthful to the cream, mixing the wormwood with the American grog. These blunders amuse the gallery who laugh at the grimaces of the inattentive players. On the walls of the small room about which we speak hang medallions bearing the names of: Bourdonnais, Philidor, Deschapelles, PH Lopez [?], Greco, P. Stamma, Macdonald, G Lolli, G Selenus; then the date of the foundation of the Café , 1718, and that of its restoration, 1855.

With the right end of the terrace is the entry to a much larger room where the most serious games are played. By around six  o'clock, all the tables are occupied. On one of them the name of Bonaparte is engraved ; it was brought from place of the Palais Royal to the new establishment. The future emperor himself had this marble chess-board made.

M . Grévy, the president of the Republic, was a long time one of the enthusiasts of Régence.  He either played or followed the games. One often sees there Mr. Paul Bethmont or Mr. Audren de Kerdrel, senator. A deputy, Mr. Fernand Gatineau, remain on the terrace as chess doesn't seem to really interest him.

Those players of which one follows the games with the most attention are: Mr. de Rosenthal, a Pole; Mr. Festhamel who, in the Monde Illustré, the National Opinion, and in the Century,  poses the most difficult chess problems; M. le vicomte de Bornier; according to the hearsay of the experts, the author of  la Fille de Roland has in just a short time become of a remarkably strong; Mr. Chaseray, appraiser, who sits endlessly in front of a chess-board at  l'Hôtel des Ventes; the sculptor Lequesne ; Mr. Baucher, the son of an equestrian professor; Mr. Charles Jolliet, whose voice fills up the room; Mr. Auguste Jolliet, from France, Mr. Prudhon of the same theatre; Mr. Séguin; Mr. Charles Royer, a well-read man who wrote the very remarkable forewords for several volumes of Lemerre. Mr. Royer is the nephew of Mr. Garnier-Pagès, whom one saw sometimes at Régence with his long white hair falling down on his immense detachable collar; Mr. Maubant, of the Comédie-Française ; Mr. de la Noue, son-in-law of the former minister for the Empire, Mr. Billaut; a retired officer and Mr. Coulon, who pushes his pieces
with military sang-froid.
 

Leaving the noisy brasseries of the Latin Quarter, we will re-cross the Seine, and direct our steps toward Montmartre, the Bohemia of modern Paris. On our way, however, we will pay a visit to the Café de la Régence, on the Place du Theatre Francais, the great rendezvous of the French chess-players. The present café is not the one where Bonaparte played, or even Alfred de Musset. The historic Café de la Régence was pulled down when the Place du Palais Royal was transformed, and the name and the habitués of the old café were transferred across the street to the present establishment, together with the table on which Napoleon used to play chess before he was Napoleon, or even First Consul. This café, thanks to its proximity, is naturally the resort of the actors of the Comedie Francaise; it has also its champion domino-player and its champion billiard-players; but its chief glory is chess, in which game the Régence has boasted a long line of champions, beginning a hundred and fifty years ago with Philidor, and continuing through Mouret, Deschapelles, Labourdonnaise, Saint Amant, Kiezeritsky, Neumann, Harrwitz, and Rosenthal, who has now abandoned the Régence, and left the chieftain-ship to Arnous
de Rivière.

In the early 1700's chess players met at the Café Procope in Rue des Fossés at the front of  the old center of the Comédie Français, owned by the Sicilian nobleman, Francois Procope. The Café Procope was a gathering place for chess players, men of letters, adventurers and spies of the police. Cafés were true cultural centers where, beyond playing and drinking, discussion about art, literature, philosophy and politics abounded. When the Café de the Régence, opened in 1718 in t the Palais Royal, it became the center of the cultural life of France. Additionally, the chess players moved there en mass.

The Café opened at the eight in the morning and its first customers were the habitual players who crowded looking to play billiards, checkers, dominoes and, naturally, chess. By noon the premises was a dense cloud of smoke from mixed tobacco and smelled of  alcohol, with the waiters needing to force a passageway through the thick crowd to the small tables where, in the course of the years, alternated such personages like Voltaire, Rousseau, Diderot, Robespierre and Napoléon.

With to the Café was born also a new personage: the professional player -  like Legal, he could be employed by the owner of the premises in order to play with anyone looking for a game, or he could be a customer himself,  playing for money. Such were the Italian Verdoni and Philidor, who divided his life between the twin professions of musician and chess-player. In the successive century, Deschapelles and the Bourdonnais were likewise. To attract the weaker players, professionals usually played at odds, giving Pawn & the move or two - even a Knight or a Rook. In the Café and the chess clubs this custom remained in vogue even into the first decades of the 1900's.

Into the middle 1800's. Paris was the pace for chess and the Café de the Régence hosted some of the more important matches of the age such as the return match between Staunton and Saint-Amant . It was just this challenge, which ended in an English victory, that marked the beginning of the decline of French dominance. By royal decision,  the Café de the Régence moved to la Place du Théâtre Français and all hope of it's former glory faded. In 1858  Morphy visited the Café and defeated with ease all the strongest local players. The golden age of French chess was gone. Chess now spoke English and, before long, will have begun to speak German.