Guillaume is the owner of a gay bar in Paris and a friend of Jacques. He saw Giovanni in a theater and was immediately taken with him. When they left, he transparently came up with an excuse to make conversation with Giovanni, and eventually got him to agree to a dinner. He employed Giovanni as a bartender, and though they had agreed that Giovanni would never sleep with him, he becomes very jealous when Giovanni begins seeing David.
Guillaume fires Giovanni out of jealousy. From that point on, Giovanni refers to him as "a disgusting old fairy" (2.3.17). After David leaves Giovanni, he goes to try to get his job back at Guillaume's bar. David imagines that Guillaume forced Giovanni to sleep with him and then still did not give him the job, but all anyone knows is that Guillaume was found dead in his upper room with the sash of his dressing gown around his neck.
In general, Guillaume is both a disgusting and a pitiful character. The younger men can't help but see him as an old predator who has to pay young boys to sleep with him. His behavior is despicable, but Jacques warns David that one day he and Giovanni will also be old men who have no control over their desires.