"My son will be an American, but I remain French," Martinez told PEOPLE in Paris on Wednesday.
The actor, 47, made the comment at the opening night of the Champs-Elysées Film Festival, where he is serving as this year's honorary president.
While joking with reporters, Martinez remarked about his experiences walking red carpets.
"It's not the first one, not the last [I've been on]," he said with a smile. "It's part of the job."