Mitterrand and Reagan don't see eye-to-eye on dealings with Libya

France, under Francois Mitterrand, is developing a more active and independent foreign policy in the Mediterranean and Africa. And, against this background, a sharp difference of opinion appears to be emerging between Paris and Washington on how to deal with Libya.

Twenty-four hours after the Reagan administration had announced it was advising Americans in Libya to leave the country, French officials in Paris were saying that France intended to resume normal relations with that country. The government of Libyan leader Muammar Qaddafi, they maintained, was no longer a subversive force.

Mr. Mitterrand presumably calculates that Franco-American relations can bear the strain that such a different approach produces because on the key issue of Western relations with the Soviet Union, his policy is much more supportive of Washington than was that of his predecessor, Valery Giscard d'Estaing.

In one sense, Mr. Mitterrand is reversing the situation between France and the United States during the Giscard d'Estaing presidency. Then, France put distance between itself and the US on relations with Moscow, but was more often than not in step with the Americans in the third world - particularly Africa. Under Mr. Mitterrand, it is beginning to look the other way round, not only in Africa but also in Latin America.

Libya, focus of last week's difference between Paris and Washington, is not the most important associate whom Mr. Mitterrand is cultivating to give thrust to his more independent policy for the Mediterranean and Africa. That role is earmarked for Algeria, where the French President paid a successful official visit at the beginning of this month.

Little noticed by outsiders during the visit was a joint French-Algerian initiative that may be harbinger of others - provided the relationship between the two countries develops as Mr. Mitterrand wants. That initiative was a French-Algerian agreement to ''guarantee'' the neutrality of Malta.

The threat to Malta was left unspecified. Ironically it is Libya, whose leader, Col. Muammar Qaddafi, has turned sour on mercurial Maltese Premier Dominic Mintoff after a spat ended the brief political love affair between the two. In particular, the Libyans are blocking Maltese exploration for offshore oil in an area in dispute between the two countries.

The French-Algerian guarantee to Malta may look like a stick applied to Libya hardly compatible with the French carrot of resuming normal relations with Colonel Qaddafi.

Cynics may say the latter move is an indecently hasty rush to position France to pick up pieces that might be abandoned by the US in Libya - particularly in Libya's oil industry.

But the Mitterrand policy toward Libya has been consistently a carefully calibrated combination of stick and carrot.

A French stick helped secure the Libyan withdrawal from Chad last month. And 10 days before US-Libyan relations reached their present height of tension (with the call to Americans to leave), French Foreign Minister Claude Cheysson was clearly indicating the imminence of a carrot.

Asked by the Paris daily, Le Monde, about French relations with Libya, Mr. Cheysson replied: ''There is now no reason why they should not improve.''

A qualified French rapprochement with Libya could, of course, serve French interests in Chad -- and indeed in the rest of French-speaking Africa immediately south of the Sahara. It could put a brake on any temptation facing Colonel Qaddafi to intervene once again in Chad or to endorse subversive activities in neighboring African countries.

Such rapprochement would also strengthen French relations with the more radical or hard-line Arab countries -- which presumably is also part of Mr. Mitterrand's intention in drawing closer to Algeria.

Both Algeria and Libya are members of the Steadfastness and Confrontation Front when it comes to any thought of negotiating or compromise with Israel on the question of the Palestinians. Yet it cannot be said that Algeria and Libya are close to each other. Algerian President Chadli Benjedid, a level-headed pragmatist, is thought to distrust Colonel Qaddafi's capriciousness.

French lines out to both of them, nevertheless, could strengthen the French hand in any French initiatives on either the Arab-Israeli conflict or the continuing guerrilla war in the Western Sahara.