Check it out ... the singer belts her heart out as she sings an all-French classic, known as "Mon Truc En Plume." Gaga seems to pay tribute to singer Zizi Jeanmaire with her performance -- which is filled with over-the-top pink feathered fans, dancers dressed in all-black, and a full jazz band.

Remember, Zizi memorably performed "Mon Truc En Plume" on "The Ed Sullivan Show" decades ago ... where she wore all-black and was joined by dancers carrying massive feathered fans. See the resemblance???

Gaga's opening number explains why she was rehearsing solo earlier on Friday ... since the only thing known about the opening ceremony was that she was set to perform Édith Piaf's "La Vie en Rose" alongside Celine Dion.

Gaga and Celine are still expected to hit the Olympics' stage together, but the opening ceremony is a lengthy affair ... so, it's likely the 2 pop stars won't duet until later in the show.

In fact, NBC's Olympics host Mike Tirico told Hoda Kotb and Savannah Guthrie on "Today" ... the opening ceremony is taking place all across Paris ... with different performances popping up as the athletes make their way down the city's river on barges.

For those worried that Celine's return to the stage won't happen, we can assure you the singer's been in Paris this week looking happy and healthy amid her Stiff-Person Syndrome battle.