I have been trying to sound her name for years and I think I am wrong.

I want to say it is "Brees-Bwah" but I have no idea.

Don't Hollywood agents tell the clients to have stage names (real or not) that are easy to pronounce?

Jean Stapleton's married name is Putch, but Jean Putch doesn't sound near as good as Stapleton.

From what little French I know, I would go with "Briz-bwah" -- but by no means am I certain...! Either way I think you have the "bwah" part spot-on.