PARIS, JAN. 11 -- Canada's Seagram Co. said today that it had applied to launch an $803 million tender offer to acquire the French cognac maker Martell and Cie., whose controlling family has indicated it would tender its shares to Seagram.

Seagram's cash bid amounts to about $535 a share at current exchange rates, based on Martell's 1.5 million shares outstanding.

The Martell family, which founded the company in 1715, indicated it would tender its 41 percent stake in the company under the Seagram offer, which would give Seagram a majority interest in Martell.

The Seagram offer tops a competing bid for Martell from Britain's Grand Metropolitan PLC, a food, hotel and beverage group that has an outstanding offer of about $768 million.

Seagram's bid will be made through its French subsidiary G.H. Mumm and Cie., the champagne company.

Seagram also has proposed acquiring Martell's convertible bonds.

Seagram's offer apparently will end a legal dispute over the company's agreement to purchase a controlling interest in the company from the Martell family.

Under the new proposal, Seagram will bid for all of Martell's shares on the open market.

"We have decided to tender all of our shares to Mumm as soon as the necessary authorizations are given and the offer begins," the Martell family said in a news release.

The family said it hoped its support of the Seagram offer would stop recent "uncertainty about the future of the company."

The family said the new bid was in the best interests of Martell, its shareholders, employees and suppliers.

The bid by Montreal-based Seagram was its second for the French cognac concern and the fourth to be launched for Martell in the past month.

The Martell battle began Dec. 16 when Seagram announced it had agreed to buy the Martell family's 40 percent stake in the cognac maker for an undisclosed price.

That would boost Seagram's total stake in the company to about 52 percent.

Grand Met quickly reacted by suggesting the bid did not conform with normal French market procedures and soon followed with its own buyout bid, which it subsequently sweetened to about $508 per share at current exchange rates, to dissuade other companies from bidding.

Seagram has said its goal was to acquire a prestige cognac producer to broaden its current line of products, which includes the Scotch brands Chivas Regal and Glenlivet, Sandeman port and the Champagne brands Mumm and Perrier-Jouvet.

Seagram said it planned to operate Martell as a free-standing unit under Seagram.

Martell posted consolidated net income of about $24.6 million at current exchange rates, in the fiscal year ended June 20, 1987, up 30 percent from a year earlier.

A big part of the rise came from the sale of its Jacomo perfume unit.

Martell's consolidated revenue for the latest fiscal year was $349 million, down 8 percent from a year earlier.

Analysts also linked that decline to the sale of the perfume unit.