For the third time in recent years, French forces are back in Chad. The reason the French have returned to their former colony is Libya's Col. Muammar Qaddafi and his ambitions to dominate this country, officially described as the world's poorest by the World Bank.

"As long as Qaddafi is around," a weary diplomat remarked, "the French know full well they are condemned to prop this country up. Even if the renewed French military presence here may produce a standoff, Qaddafi will try again once the French pull out."

But if by now the various players are used to the game, that does not mean that they all play by the same rules.

Qaddafi, in the view of observers, seems determined to install a government friendly to Libya in this battered capital and then use it as a springboard to promote wider ambitions south of the Sahara.

Chad's President Hissene Habre, a former Qaddafi ally, is committed to driving the last Libyan soldier out of the northern third of a country the size of New Mexico, Oklahoma and Texas.

Chadian government troops killed 864 enemy soldiers and wounded 456 in fighting in the north of the country Wednesday, Foreign Minister Gouara Lassou said last week, according to Reuter. He said 18 Chadian forces had been killed and 64 wounded.

[A rebel spokesman in Paris confirmed the fighting but said the rebels remained in control in the area.]

In the current Operation Sparrow Hawk, France has sent fighter-bombers, interceptors and airfield perimeter defense troops here to prevent a Libyan takeover of so-called "useful" Chad -- the southern half of the country.

But France, especially in the final stages of legislative elections, is in no mood for a wider war with Libya, which, since 1973, has occupied the so-called Auzou strip south of the internationally recognized Chadian-Libyan border.

Specifically, France wants no part in helping Habre achieve a goal that its officials insist would strain the logistical capacity of an already expensive expeditionary force.

"We want to calm things down, not solve the total problem," a French diplomat remarked privately.

Habre, pleased with his own recent victories over Libyan-backed rebels in the north and the renewed presence of French warplanes in the capital, is confident that France will protect "useful" Chad with its aerial umbrella. Even if the French right wins the elections, Habre said at a recent news conference, he is confident a new government would continue to aid him.

"France is France," he said, "thanks to the role she plays in the world, especially in Africa."

That was diplomatic shorthand putting French President Francois Mitterrand on notice that conservative black African leaders such as Felix Houphouet-Boigny of the Ivory Coast and Abdou Diouf of Senegal could be counted on to speak out if French resolve weakened.

Such is the price of credibility for French governments, which without exception have extended protection to the former colonies of France's black African empire since formally hauling down the tricolor flag in 1960.

Since the Nixon administration, under criticism in the United States for its involvement in the Vietnam war, watched French public opinion accept the first military intervention here nearly two decades ago, to help control internal divisions before Qaddafi had come to power in Libya, U.S. governments have envied Paris the lack of parliamentary carping over black African affairs.

As for the Reagan administration, so deep-seated is its suspicion of Qaddafi that Washington reports suggest some officials hope to use Chad to bleed the Libyan strongman economically. Americans with more immediate knowledge of Chad appear quite content to play a backup role to France, especially at a time of pared-down U.S. foreign aid.

For French taxpayers, bailing out Chad, whose estimated annual per capita income is $88, has always been costly and is going to become more so.

The military costs are high, as French transport planes on their way here from France must detour expensively around off-limits Algerian and Libyan airspace. Aviation fuel for the French warplanes here is being flown in from neighboring Cameroon by commercial aircraft.

Also, the world price of cotton, traditionally Chad's only significant foreign exchange earner, has collapsed this year.