Just over a month ago, Francois Mitterrand easily won re-election for a seven-year term as president of France, but parliamentary elections this past weekend seem to assure that his Socialist Party is not going to have an easy time ruling the country.

The Socialists did gain 62 seats and knock a coalition of right-wing parties out of control of Parliament, but Mitterrand's party also fell 13 seats short of a majority, although it is by far the largest single group in the French National Assembly.What this means is that for the first time in 30 years, neither the right nor the left has a clear majority. The only way to govern is for some kind of cooperation between left and right, almost always a difficult task.

Mitterrand had called for the election on the heels of his own success at the ballot box, obviously hoping to use that as a springboard to vault the Socialist Party into power. However, his personal popularity did not translate into victory for his party.

Yet in the complicated mixture of political groups in France, it turned out to be an election that nobody won, although the Socialists emerged stronger than anyone else. The radical fringe was the big loser. The Communists lost eight seats, leaving them with 27; the far-right National Front lost 34 of its 35 seats.

The lineup now has the Socialists with 276 seats, and a grouping of rightists and center-rightists with 271. Unfortunately, this leaves the Communist Party with its 27 votes, in a position to wield influence far beyond its shrunken numbers.

Given the fractured nature of Parliament, France probably is going to have to be governed on an issue-by-issue basis, but Mitterrand has considerable power as president - more than a U.S. president has with Congress - so the government may not be as shaky as those coalitions that govern Italy and fall apart with regularity.

About the only clear thing to come out of the whole thing was summed up by the French newspaper LeMond, when it said that the biggest casualty of the election was arrogance. "Now, nobody can pretend to incarnate the will of the people."

That may promote humility, but government by coalition always has its pitfalls. A muddled and divided multi-party government where no one is clearly in charge can also result in a kind of political paralysis - which could handicap France and its Common Market neighbors.