Despite the both being Allied Forces characters, there is little exploration of their relationship. However, they both go along well and are good friends. Russia is proven to see France as a person worth seeking advice from.
In a relationship note between the main Allies, Russia is said to ask advice from France on how to make friends. He follows (stalks) France because he is shy to ask him directly. France finds it both terrifying and precious when he finds out where does the scary aura behind him comes from.