France has warned the United States of possible damage to bilateral relations if the Pentagon selects a British firm over a French company for a $4.3 billion contract to modernize the U.S. Army's battlefield communications system, foreign diplomats said yesterday.

A diplomatic note delivered Wednesday to the U.S. Embassy in Paris by French foreign and defense ministry officials said France had legitimately outbid British competitors and deserved to win the right to supply a mobile, wireless telephone system, diplomats said. A copy of the note reportedly was sent to the White House.

The warning marks the latest turn in what has become a bitter British-French rivalry to land the largest, single U.S. military contract opened to foreign competition.

Army officials have recommended the less costly and older French system, but Defense Secretary Caspar W. Weinberger delayed his decision after British Prime Minister Margaret Thatcher appealed to President Reagan to choose the British model, calling the contract "extremely important" to her nation, according to U.S. officials.

Plessey Defense Systems, a London-based military electronics firm, reportedly has asked the Defense Department to reopen bidding to consider a significantly less expensive offer to supply its Ptarmigan system. Its U.S. partner is Rockwell International Corp.

Thomson CSF, of Paris, whose U.S. partner is GTE Corp., argues that the bidding process has already shown the technical superiority and economy of its RITA, an acronym for Reseau Integre de Transmissions Automatique.

In her Aug. 30 letter to Reagan, Thatcher emphasized Britain's reliability as an ally. Her government supports such controversial Reagan programs as the Strategic Defense Initiative, which France opposes.

The French diplomatic note pointed out France's role as a good ally and warned of a strain in relations if the Pentagon skewed the bidding process by rejecting Thomson's bid.

Guy de la Chevalerie, a spokesman for the French Embassy here, declined comment on the letter. But foreign diplomats said it was motivated by Thatcher's unusual appeal, which, according to one source, "put technical competition on a political level."

"The French were obligated to respond," the source said.

Reagan administration officials cite the contest for the Army's Mobile Subscriber Equipment program as an example of the "two-way street" relationship it intends to enter with allies who buy U.S. military equipment. The Pentagon decided to buy a foreign system to avoid the costs and time to develop a U.S. model.

U.S. officials who favor Thomson view the contract as an opportunity to wean the French defense industry from its traditional Third World customers.