Why not polite friendship; here is a definition that match my understanding of the French expression.
The main distinction between a “polite friendship” and a “deep friendship” is competition. If you are truly in someone’s corner, and you are showing up to the friendship with a desire to see Kingdom come in that person and in that friendship, your friendship will have lasting roots of authenticity and respect. And unless you have surrendered every bit of personal gain to God, the competition will try to find a way into your friendship. Just a little spark of competition can poison an entire friendship.