TheFork users who ate in Saint-Priest have said really good things about Le Cocon - Double Tree by Hilton, L'Alpage and Café des Artisans, Le Bouchon de Muriel - Quartier Sans Soucis. Maybe you should give them a try!
Some of the more popular Bouillabaisse restaurants where you can go with your pets in Saint-Priest according to TheFork users include:
Le Cocon - Double Tree by Hilton, with a 8.6 rating
L'Alpage, with a 8.6 rating
Café des Artisans, Le Bouchon de Muriel - Quartier Sans Soucis, with a 8.5 rating