Auxiris: From my experience of French type dances, at festivals in England, I can't see singing in the intervals as fitting in too well.
I'd have thought that an alternative way would be to have a singing room away from the dance hall. That's the way singing finds a space in the Fleadh Ceoil, upstairs from the wild music people singing Sean Nos in a separate bar.
In France I'd have thought you might do that, opening it both to traditional folk singing and the chansonnier tradition.
The other thing that occurs is, do people in France ever have Cajun dances? Because of course all the cajun bands I've seen use songs with the dancing. Enormous fun, but also it might help people think of singing as something that they might try some time.