In what year was the French Open founded?

The French Open was founded in 1891.

The tournament began as the French Championships, a national club competition held in France. Its first edition was restricted largely to players who belonged to French clubs, so it was not yet the globally open Grand Slam event familiar today.

The competition became international in 1925, when it opened to amateur players of all nationalities and was recognized as a major championship. It moved to the Stade Roland Garros in 1928, and the name “French Open” became associated with the event after professional and amateur players were allowed to compete together in 1968.

This history explains the common alternative answer of 1925. That year marks the tournament's transformation into an international major, not its founding. Likewise, Roland Garros refers both to the venue and to the aviator whose name the stadium carries; the competition itself predates the stadium by decades.