TheFork users who ate in Avignon have said really good things about Le Paon Gourmand, Pizza Cosy and Basta Cosi!. Maybe you should give them a try!
Some of the more popular Pizza restaurants that offer vegetarian options on their menu in Avignon according to TheFork users include:
Le Paon Gourmand, with a 9.5 rating
Pizza Cosy, with a 8.5 rating
Basta Cosi!, with a 8.9 rating