Ken Roe writes on Cinema Treasures: "The Cinematophone Modern Theater was opened by Alexandre Rota in October 1906. ... It was designed by architect J. Fanon of Lyon. The Cinematophone was an early record player which was used to provide background sound to silent films. It was used in the name of the theatre to promote the fact that the Modern Theater had it installed."
Cinématophone does not seem to have existed in any other French city at the time.
Alexandre Rota was born in Candelo, Lombardy in 1868, he appears as a “patron weaver” in the 1901 census in Lyon. He was as the director of the Bellecour cinema in Lyon in 1905. In October 1906, he opened another cinema hall - the Cinématophone-Modern-Theater.
He wrote about his activities: "Development of cinematography in all its forms - Purchase, sale, rental of devices, new and second-hand films - Rental of films from 0 fr 01 per meter and per day - Home screenings, fixed price for one or more screenings - Treaties for the end of shows in casinos, music halls, concert halls, boarding schools, lounges and families - Photographs, light projections - Fixed price installation of cinematographic stations - Advertising by the cinematographer - Electricity - SGDG patent for cinematographic projection in broad daylight".
Alexandre Rota, an entertainment entrepreneur, also an engineer, patented for having apparently made it possible to organize open-air cinema sessions in the middle of the day. He had obtained a gold medal at the Congress of Inventors of Lyon in 1911. It is known that Alexandre Rota knew how to handle a camera. He thus manages to show in his cinema a film on the funeral of Cardinal Coullié, shot by him that very morning. [Source]
Philippe Célérier writes more about this cinema on his blog:
"The original 400-seat hall (only 230 in 1961) looks a lot like a theater, with its two side galleries.
The establishment often changed its name: Modern'Cinéma from 1936 to 1953, Duo from 1953 to 1979, Modern '39, then finally Petit Coucou from 1979 to 1985. Its programming will also experience a lot of upheavals: if in 1958, the Duo is the first art house in Lyon, the Petit Coucou will move towards another genre of cinema, even being classified X in 1979 and 1982, before closing its doors definitively in March 1985 ..."
A. Rota was also a good salesman, when he used the popular postcard as advertising. Maybe the man in the little picture is Alexandre Rota himself? Surely he doesn't stand there by chance.