The €2bn price tag is twice the amount the publisher takes in annual sales. Vivendi would receive a one-time gain of €800m (£503m) from the sale, which it wants to put towards its $2.2bn (£1.5bn) purchase of US textbook publisher Houghton Mifflin.
The two companies are believed to have signed a letter of intent and the sale is expected to be completed by the end of October, once due diligence has taken place.
The deal will give Cinven a raft of French-language specialist publications, including medical titles Staywell and Le Quotidien du Medecin. The purchase also includes UK title Property Week.
In a statement, Vivendi said, "Cinven's offer, which includes the health publications, is the most favourable. It's also the most coherent, as it allows Vivendi Universal Publishing's trade arm to continue as a standalone unit."
The agreement marks a new adventure in the publishing world for Cinven, having only sold IPC to AOL Time Warner's Time Inc for £1.15bn two months ago.
Vivendi announced it was selling its trade titles in June, when it successfully bid $2.2bn for Houghton Mifflin.
IPC's former parent Reed Elsevier also bid for the Vivendi titles, alongside Bertelsmann and VNU.
Vivendi now has to find a buyer for its classified advertising business Comareg, which is expected to fetch €400m (£251.5m).