BARELY two months ago, French President Fran,cois Mitterrand faced a restive public, dissatisfied on the domestic front and egged on by cries of ``10 years is enough!'' from a few influential individuals and publications. Even some of the faithful within Mr. Mitterrand's own Socialist Party began looking with dread toward 1991, which marks a decade of the Mitterrand presidency. Having just seen Margaret Thatcher, Britain's 11-year prime minister, toppled from office, party regulars spoke worriedly of ``the 10-year syndrome.''
That was before the Gulf war, however. After pursuing a policy toward the crisis approved by 4 out of 5 French citizens, and especially after a series of televised messages that revealed a determined leader, Mitterrand's approval rating hit 75 percent.
Many predict, however, that this popularity will begin falling soon, that the disarray of French political parties will continue, and that the electoral tests the Mitterrand presidency faces before its second seven-year term ends in 1995 are potential dark spots.
``The French people were reminded [by the Gulf crisis] that they have a president of international stature,'' says Guy-No"el Abraham, a communications consultant in southern France and a Socialist Party activist. ``Now I think that popularity will taper off as domestic issues return to the forefront.''
Such thinking, along with Mitterrand's desire to put new wind in the sails of domestic issues, has built up speculation that Mitterrand will replace Prime Minister Michel Rocard by midsummer.
Many analysts say Mitterrand is haunted by the possibility of a conservative victory in the 1993 legislative elections, an outcome that would force him to relive the ``cohabitation'' he unhappily endured from 1986-88 with Gaullist Jacques Chirac as prime minister. Any decision to change heads of government will be determined, these analysts say, by the priority of winning a ``presidential majority'' in 1993.
WITHIN the Socialist Party, some activists believe Mr. Rocard could be replaced by Defense Minister Pierre Joxe who, like Mitterrand, has benefited from the Gulf war victory. Some feel Mr. Joxe's firm stance against Iraq's aggression and his left-leaning perspective on social issues may be an appealing combination to the public right now.
Others who consider Rocard on his way out say the country's political state of mind means he can only be replaced by another centrist. That, plus the fact that much of Mitterrand's post-Gulf popularity gain has come from the right, has led some to speculate that he could even go outside the Socialist Party to choose Raymond Barre, former prime minister under Val'ery Giscard d'Estaing, to try to consolidate that popularity.
Despite such speculation, however, many analysts believe Rocard is likely to stay where he is until the 1993 legislative elections. ``Rocard has been a disappointment, you can see it in the number of people who ask, `What has he done, what does he want to do?''' says Colette Ysmal, a specialist in French politics at the Center for French Political Studies. ``But Mitterrand has no one to replace him, and that is one of the president's problems.''
Mrs. Ysmal believes anyone else is either too far left or too far right to serve Mitterrand's electoral purposes. As for former Prime Minister Laurent Fabius, Mitterrand's recognized protegee, she says naming him now would be ``too dangerous.'' The Socialists will lose regional elections next year because the regions remain a rightist stronghold, says Ysmal. ``Naming his preference just before an electoral defeat wouldn't make sense.''
France is likely to preserve a ``more or less 50-50'' right-left electoral split that will dog Mitterrand through the legislative elections, Ysmal says. She agrees with other analysts that the lack of violent reaction by - or toward - French-Arabs during the Gulf crisis could be a good sign for integration efforts.
Still, she predicts, neither that possibility nor the anti-Gulf-war stance of Jean-Marie Le Pen will have much negative impact on Mr. Le Pen's far-right, anti-integrationist National Front.