The new president of France, Francois Mitterrand, has overwhelming political reasons not to embrace the United States in a hurry. So why has he sent his foreign minister to this country for a round of full-dress diplomatic talks?

The answer is that Washington, not Paris, sought the encounter. That reaching out suggests the Reagan administration is far less rigid than generally supposed in its attitude toward European Socialists and the nonaligned countries of the Third World.

The pressing task before Mitterrand is to build a majority, or at least a working minority, in the elections for a new French Assembly scheduled for June 14 and June 21. To do well, his own Socialist Party will have to take away votes from Communist candidates, so Mitterrand has to avoid the appearance of diluting the basic left-wing program. For that reason, he originally planned to put off any official contact with the Reagan administration until after the coming election.

But President Reagan and Secretary of State Alexander Haig had other ideas. When Chancellor Helmut Schmidt of West Germany visited Washington last month, they sent word back to Mitterrand that they would like an early visit from his foreign minister, Claude Cheyson. A kind of cover for the visit -- a reason that could not displease left-wing Frenchmen -- was even agreed upon. Thus Cheysson, during his visit here, is expected to make a fuss about the harmful impact of high American interest rates on the economy of France and the rest of Europe.

That complaint is supposed to camouflage harmonious discussion on several larger points. First, the Reagan administration wants to convey to Mitterrand its full confidence in his intention to stand up to the Communists in France and the Russians in Europe. As one very high administration official put it:

"The Socialists have been fighting in the streets against the Communists for years. We believe Mitterrand will squeeze the French Communists. We think he is going to be very tough in dealing with the Russians."

Second, the Reagan administration wants to urge a cautious approach to economic policy. "All of Europe," the same official said, "faces extremely difficult economic conditions. We know that while they were in opposition, Mitterrand and the Socialists compile a hit list of industries they wanted to nationalize. We think it makes sense to go slow, to get a feel for governing, to build confidence before starting panic."

Then there is the matter of the Third World. Cheysson is a diplomat renowned for his connections in Africa and Asia. He goes further than Mitterrand in sympathy for many left-wing regimes in the southern continent, and in his mistrust of authoritarian governments. The Reagan administration is prepared to open a dialogue with the Mitterrand government on the Third World. It wants to hear Cheysson's ideas on how economic help might induce some Third World countries to disengage from connections with Russia, Cuba or Libya.

Finally, to continue the dialogue, the Reagan administration seeks an early session between the president and Mitterrand. There is some thought here of an official meeting after the summit of advanced countries in Ottawa next month, or of a get-together in Williamsburg, Va., in the fall. But nothing has been decided, and the choice is being left to Mitterrand.

A distinct calculation explains this show of harmony. The Reagan administration wants to grasp Mitterrand, in the words of one State Department official, "by his right hand." The hope is that American confidence will cause him to align France with this country and its allies, especially West Germany. That approach is not without risk. The French president and his advisers are soft on at least some leaders the United States regards as dangerous -- notably Castro. They take a dim view of others whom Washington seeks to cultivate. Thus disappointment is possible, and the hand is not easy to play. Because he is so experienced, it might be useful to keep on in Paris, at least for the early stages, Ambassador Arthur Hartman, who is scheduled to go to Moscow.

Still, the basic fact is that the United States and France have a lot of business to transact. Whatever the outcome, it is no bad thing to begin in a cordial atmosphere.