The verb is "tutoyer".
Let's say you, Gerry meet Pascal. You start using "vous" because you don't know each other. (Vous vous vouvoyez au debut). Then, you realize you are the same age, there is a great rapport between the two of you, and you decide to ask him "Est-ce que nous pouvons nous tutoyer? " or "Peut-on se tutoyer?" (a little more colloquial) Or even "Je peux vous tutoyer?" (Note that "se tutoyer" is a reflexive verb).
Hope this helps,
Sylvie