juste une idée.

I think that this would be sufficient, without going to the extremes of saying "nous nous tutoyons" (we use the familiar form of you).

une autre façon de le dire

autre hypothèse : le traitement informatique, le classement ou la recherche se fait sur la base du prénom

There are two levels of address in French: the "tu" (thee) and the "vous" (you). The "tu" is used to speak with familiarity, the "vous" shows or expresses a greater distance between yourself and the person being adressed (i.e. more respecful or distant). The two forms are referred to as "se tutoyer" (from the two forms: "tu" and "toi") and "se vouvoyer".

I've never heard the phrase "on a first-name basis" literally translated or anything that sounds like it being used either in media or on the street here in Canada. Also, no one would even think of adressing someone by their full name (Madame Tartenpion) while using a "vous", so theeing someone implies you can use their first name.

The phrase "on peut se tutoyer" ("we can..." or "I give you permission to thee me") is the same saying "call me by my first name".

And finally, despite the fact that French Canadians "tutoie" much more than on the Continent, in Canada, "on se tutoie" means "we speak to one another with familiarity".