Has the Socialists' patient, long-term strategy, that finally produced landslide victories for President Francois Mitterrand and his party last spring, suddenly run out of steam?

The fact that France's political analysts are asking that question, however tentatively, is considered more important than the still partial results of the local election yesterday, in which the conservatives outpolled the combined Socialist and Communist totals. Runoffs for the election are scheduled for Sunday.

The conservative opposition broke the left's string of victories, although the Socialists remain strong enough on a national level to govern by themselves for the next four years and Mitterrand's mandate does not expire until 1988. The first-round outcome, nonetheless, constituted a warning to the government.

The left's strategy has come undone largely because the Communist junior partners seem incapable of providing enough strength to provide the alliance with the Socialists an overall majority in the future.

When Mitterrand took control of the discredited Socialist Party in 1971 he argued that an alliance with the then more powerful Communist Party was the only way to achieve power.

In local, municipal, national and presidential elections since then, the Socialists gradually outpaced the Communists. Even yesterday they confirmed their claim as France's largest political party.

The whole logic of the Fifth Republic constitution, hand-tailored for founder Charles de Gaulle, appeared to ensure that moderates would hesitate to vote for a presidential candidate from the leftist spectrum for fear of Communist influence.

Yet by last year many conservatives and moderates, fed up with 23 years of nonstop rightwing power, supported the Socialists and voted against incumbent president Valery Giscard d'Estaing as much as they voted for Mitterrand. They also solidly supported the Socialist Party in the June 1981 legislative elections, thus ensuring it would outpace the Communists and give Mitterrand a solid base for ruling France.

In the process, the Socialists won an outright majority in the national assembly. The Communists, who polled less than half the Socialists' 37.7 percent in the vital first-round legislative elections, were given four Cabinet posts. The Socialists were convinced that having the Communists in the government was the best way to keep control over them.

The Communists traditionally do better in the cantonal, or local, elections than in the national contests. Yet yesterday, the Communist Party was reduced to 15.87 percent of the vote.

That was its worst showing in a cantonal election, almost seven percentage points below 1976 and 1979, only half a percentage point better than its showing in the 1981 presidential race and a half point below its legislative election showing.

Even Jean-Pierre Chevenement, the technology minister who once had close ties to the Communists, recently advocated "widening the majority" to attract moderate voters.

With Socialists and Communists calling today for a maximum turnout next Sunday to sweep the seats not won outright yesterday, the left still has a chance to save face.

Yet even Jacques Fauvet, the director of the pro-Socialist newspaper Le Monde, suggested that a "smaller ministerial team, a more coherent policy, a more present president would help convince that part of public opinion which does not refuse change, but fears upheaval."

Inevitably, analysts have wondered if the vote yesterday will prompt Mitterrand to order a "pause" in the reforms such as moderates in his camp have called for. But Communist leader Georges Marchais has said reforms should be pushed ahead even faster, thus raising fears here of the Communist-dominated trade union conducting wildcat strikes to destabilize the Socialists and their government.