The move follows the Fr2.6bn takeover of Cooper's main rival, Office Pharmaceutique Francaise, by Germany's Gehe. Cooper had made an unsuccessful counter-offer with Bergen Brunswig, a US group.
The deal, which would improve its access to France's 22,000 retail chemist shops, could help Rhone to ward off the effects of a clampdown on state health spending.
Cooper's management has been trying to fend off stake-building by Claude Gros and his Sabeton group.
By last summer, Sabeton, which strongly opposed the bid for OCP, had acquired 14 per cent of Cooper's capital and 20 per cent of its voting rights after Mr Gros persuaded a court to freeze the rights of two Cooper units that held 18 per cent.
Rhone is offering Fr2,400 per share in cash or 18 Rhone shares for one share in the unlisted distributor. There was no immediate sign of any rival bids.
A Rhone spokeswoman said that, ignoring the 18 per cent held by the two Cooper units and legally frozen, the acquisition should cost between Fr2.8bn and Fr3bn. Cooper had sales of Fr2.3bn in 1992.
Rhone's US unit, Rhone-Poulenc Rorer, manufactures Doliprane, the paracetamol brand, exclusively for Cooper. Doliprane is the biggest- selling drug in France, in terms of pills sold, and has annual sales of Fr500m. Institut Merieux, another Rhone unit, supplies Cooper with Vaxigrip flu vaccine.