While having lunch with a friend, out of the blue she started talking about how to sing the neutral vowel, especially in French. The neutral vowel is the one where your tongue just lays there and you lips don't do much of anything. Uh. What people say when that can't think of anything to say.
The problem with French is that you frequently sing these even when you wouldn't say them. So you can't make your decision based entirely on what people say.
My friend teaches her students to use a bit of tongue in the pronunciation, a little like the "u" in "La plume de ma tante."
I don't have an opinion. I try to form opinions based on empirical data. If I listen to Magdalena Kožená singing in French, she sings it like my friend suggests. So do a lot of non French singers.
However, if I listen to French people singing, people like Régine Crespin and Véronique Gens, it's just plain "uh." Like the "de" in "La plume de ma tante." I am always struck by how when a French person sings French, it sounds perfectly normal, but when someone else sings it, it often sounds quite odd. This is probably one of the reasons. If Régine Crespin is doing it, it's probably right.