Find my grandpas French birth records

[alanATX]

Hi all, it's been really difficult to find any birth records for my grandpa, who was born in 1922 in Paris, France (allegedly). His full name is Maximino Carlos Alberto Gonzalez Gagnebin, which is quite a mouthful.

He was born on February 26th, 1922, in Paris, France. A couple of years later his father/mother moved to Mexico. Father, Manuel Gonzalez, and his mother Fernanda Gagnebin. Manuel moved to Mexico to enlist in the military. What's interesting is I was able to find a record in the Mexican civil registration births for my grandpa (Max) , and in it it says that my grandpa was indeed born in Paris, France on February 26th, 1922. His name in that register is listed as "Maximino Gonzalez y Gagnebin."

Seems I'm not able to find his name in French birth records because there are so many variations of the spelling of his name. Pretty much every name of his has a French alternate and it's making it incredibly difficult to track him down. Like when I search for his mom, Fernanda Gagnebin, it gives me different flavors of her last name. On top of that, people in my family are telling me Fernanda was born in Switzerland but lived in France.

If anyone has suggestions or can help me find his record that would be helpful. Happy to provide any other info.