MITTERRAND FACES TOUGH `COHABITATION'

French President Francois Mitterrand, who plays a round of golf every Monday morning, may want to spend more time on the golf course in after France's national elections this month.

The French right has already warned Mr. Mitterrand that the anticipated "cohabitation" period, when the Socialist president is expected to face a right-wing prime minister, government, and parliament, will be more difficult for him than the cohabitation of 1986-88. This time, sensing Mitterrand's low popularity and his lame-duck status, the right intends to assert itself.

Just how difficult the right can make things for Mitterrand will depend in part on the magnitude of its election victory. But already, some right-wing leaders are calling for the president's full submission.

"If the president refuses the choice of the French people and all the governing powers that choice entails, then I am for forcing him to resign," says Andre Soullier, a Lyon attorney and a center-right candidate for the National Assembly.

"I am severe," adds Mr. Soullier, who says the right is showing signs of being too soft on Mitterrand. "Either he submits, or he quits."

Nothing in the French Constitution requires Mitterrand to follow Soullier's advice. But Soullier says the new parliament, especially if the right wing holds 80 percent of the seats, can make life impossible for Mitterrand if it chooses.

To do this, Soullier says the parliament could simply refuse to confirm the candidates for prime minister the president proposes - Mitterrand has already said he will choose a prime minister from the party winning the largest percent of the vote - or could "force Mitterrand against a wall" by voting for laws he could not accept.

How the public would view such tactics is unclear. Despite Mitterrand's rock-bottom standing in voter surveys, other polls show the French do not want the kind of government crisis Soullier is proposing.

Besides, it may not be in the best interests of the right's presidential ambitions to wreak havoc. With difficult problems awaiting the new majority and Mitterrand's full term up in two years, the right just may want the Socialist president around as a bogeyman for the 1995 elections.