He said: "Brive have really welcomed me to the club. I'm a competitor and I will try to use my experience to help the club.
"It's a new challenge for me and I know that I will have to find my place in the team."
Cohen was a member of the Barbarians squad who beat South Africa at Twickenham on Saturday, his first competitive game of the season.
He quit Northampton after being overlooked for the club captaincy and will look to help his new club arrest a slide that has seen them lose their opening four Top-14 matches.
Cohen has scored 31 tries for England - only Rory Underwood has more - and was a member of the 2003 World Cup-winning team.