Evidence of rapidly escalating Libyan military involvement in Chad has posed a severe test for France's Socialist government in its relations with Africa.

As the former colonial power for much of sub-Saharan Africa, France is intimately concerned with the latest upheavals in the region. Many of the conservative French-speaking states of black Africa are alarmed by what they see as the aggressive designs of Libya's Col. Muammar Qaddafi and look to Paris as the ultimate guarantor of their own security.

The new crisis has created delicate political and diplomatic problems for President Francois Mitterrand, who came to power in 1981 promising to put France's relations with black Africa on a new basis. While in opposition, he had been fiercely critical of French military intervention on the continent and was determined not to repeat the mistakes of his predecessors.

Once in office, Mitterrand quickly distanced himself from much of the Third World idealism of the left wing of his Socialist Party and reassured worried African leaders that France was fully aware of its responsibilities. In return, black Africa has given him, as it gave previous French heads of state, the chance to shine as an international statesman.

Mitterrand has, however, balked at increasingly desperate calls for French troops or fighter planes to be sent to Chad to support the government of President Hissene Habre against Libyan-backed rebels. Keenly aware of a long history of futile French military expeditions to the landlocked state, he chose a more discreet form of intervention by airlifting weapons and other military supplies.

For a time, this cool-headed response seemed to be working. Bolstered by the inflow of arms, Habre was able to launch a counteroffensive against the rebel army of former president Goukouni Oueddei. By last weekend, he had won back practically all the territory lost in June and July, including the northern oasis town of Faya Largeau, and captured several hundred prisoners.

It was then that Qaddafi increased the stakes by sending his Soviet-built MiGs on bombing missions over Faya Largeau, effectively trapping the bulk of Habre's 4,000-man Army. The French government once again received urgent appeals from Ndjamena, Chad's capital, for direct military assistance--and once again chose to react cautiously by sending antiaircraft weapons.

Added to the appeals from Chad have been increasingly urgent calls from the Reagan administration, which sees its own potential for direct intervention there as limited and feels that France must carry the ball. When the current round of fighting began, Washington watched with approval as Mitterrand responded gradually to the gradual escalation in the fighting.

"The French did it right," said one administration official in Washington, "letting Libya escalate until they respond." The trouble now, in Washington's view, is that the time for a strong French response has arrived, and the French are not playing their part.

By increasing American military assistance to Chad, this U.S. official said in reference to the $25 million now promised by Washington and the dispatch of three U.S. military trainers, the administration hopes to increase its own leverage on the Mitterrand government.

"To induce the French to do what they have to do, what we want them to do, we have to be there at the table," he said.

But U.S. hopes that France will increase its participation by answering Chad's appeal for French aircraft to counter those of Qaddafi merely have added to Mitterrand's dilemma.

If he sends Jaguar fighter planes based in Africa, he will in effect be giving up his own declared policy of avoiding military intervention. He would also run the risk of a direct military and diplomatic confrontation with Libya, with which France has been trying to improve relations.

By playing it cool, on the other hand, Mitterrand risks seriously damaging France's reputation in black Africa if Habre is defeated. There is also the possibility that the United States might feel obliged to fill the vacuum in what traditionally has been regarded as a French sphere of influence.

According to French officials, leaders of conservative African states near Chad have been on the phone to Paris regularly in attempts to persuade Mitterrand to act more forcefully. This concern was reflected in a recent editorial in the semiofficial Ivory Coast newspaper, Fraternite Matin, urging France to reconsider its refusal to intervene directly.

Describing Habre's appeal for French planes as "an SOS," the paper said that not to respond positively could only be regarded as a "refusal to give assistance to a friend in danger of death."

Misgivings in conservative African states about France's relatively low profile in Chad are likely to be enhanced by today's coup in Upper Volta. There is no evidence of direct Libyan involvement, but the young Army officer who seized power in Ouagadougou, Capt. Thomas Sankara, is known to admire Qaddafi.

Choosing the wisest course of action in Chad has not been made any easier by the wildly contradictory reports of the fighting there and the difficulty of guessing Qaddafi's intentions. French officials believe that the Habre government has at times exaggerated the Libyan threat in order to drum up support from abroad and that the situation on the ground is not desperate yet.

An indication of the uncertainty felt here was provided today by an editorial in Le Monde saying that France was no longer able to guarantee the security of its former colony by itself. Pointing to the dispatch of a small number of American military advisers, the newspaper said this could compromise the credibility of "the French umbrella" in other African states.

There is an obvious difference of emphasis in Paris and Washington over the nature of the crisis in the sub-Sahara. French officials privately describe the U.S. preoccupation with Qaddafi as exaggerated and have refrained from criticizing the unpredictable Libyan leader in public, preferring to rely on the techniques of quiet diplomacy.

In the view of seasoned officials in Paris, the conflict in Chad is essentially a civil war between chieftains that has been going on sporadically for nearly 20 years. Le Monde has dubbed it "the endless safari." The American view seems to be that it is a case of naked Libyan aggression against a pro-western government.

While formally denying that any French soldiers are in Chad, the French government has taken measures to ensure that it can intervene in the case of dire necessity. The Defense Ministry has confirmed that a force of 165 French paratroopers is on standby across the border in Cameroon ready to evacuate foreign civilians from Ndjamena.

France has 7,500 troops and military advisers stationed permanently in its former African colonies. The largest bases are in Gabon, Central African Republic, Djibouti, Ivory Coast and Senegal, with which France has formal defense agreements.