Paris — France has its own ''Falklands'' troubles. Just as with Britain, the remnants of the French empire span the globe. ''Home'' to 1.6 million Frenchmen ranges from the tiny islands of Wallis and Futuna, smack in the middle of the Pacific, to the tiny islands of St. Pierre and Miquelon off Canada's eastern shore.
Since no Canadian junta is likely to order an invasion of St. Pierre and Miquelon, there is little fear of a foreign attack. Instead, the most serious threat to French rule in the far-flung specks of what was once a mighty empire comes from disgruntled local inhabitants.
And that is the reason Francois Mitterrand's Socialists have recently held local elections and given the most populous of France's overseas possessions more autonomy.
For centuries, Paris ruled its empire with an iron hand, treating Polynesia and the Perigord as one and the same under the law. In the 1950s and early '60s, though, most of the empire, including Indochina and North and West Africa, gained independence.
Conservative governments gave the smaller of the remaining possessions, the so-called ''territories,'' considerable autonomy in the 1970s. But the larger remnants of the empire, the overseas ''departments'' - including Martinique, Guadeloupe, La Reunion, and Guiana - remained under the firm control of Paris.
In recent years, it has become clear that French rule does not suit some overseas citizens. In 1980, in Guadeloupe, just before President Giscard d'Estaing was to visit the island, the main courthouse and local assembly were bombed and an Air France jet was blown up.
Most volatile has been the Pacific territory of New Caledonia. In January of this year, independence-minded native Melanesians ambushed and killed two French gendarmes. A year before that, armed French settlers had stormed into the local assembly to protest any weakening of the territory's links with the mainland.
To defuse these bubbling, violent pressures, the Socialists are making the empire more autonomous. Last month's elections of the first local assemblies for the four departments were their first move in this direction.
''We are giving these residents the chance to run more of their own economic and cultural affairs,'' said Jacques Fournet, political counselor to the secretary of state of the DOMTOM (Departements et Territoires d'Outre-Mer). ''Most of the population wants to retain its attachment to France,'' he explained, ''but we have to recognize their right to difference.''
The conservative opposition disagrees. It sees autonomy as leading to more instability.
''After 200 years of (French) rule, the government has rashly taken a certain number of measures which separate the constitutions of the overseas departments from those of the mainland departments,'' complained Pierre Messmer, former prime minister and chief opposition spokesman on the issue. ''This will create doubts in the minds of the Frenchmen who live in these departments.''
DOMTOM officials say, though, that the elections neutralized the independence movements. Independence candidates picked up less than 5 percent of the votes in Guadeloupe, Martinique, and La Reunion. They received just a bit more in Guiana.
Moreover, the officials see the results as a ratification of their autonomy plan. The Socialists did better than expected, winning a majority of the votes in what traditionally have been conservative strongholds.
''The opposition's main campaign weapon was fear,'' DOMTOM's Mr. Fournet said. ''But the election results show that the departments are satisfied with this injection of autonomy.''
As a result of the success, the Socialists plan to press forward with further reforms in New Caledonia. To head off the grievances of the native Melanesian minority, Mr. Fournet said land reform and other economic measures favoring the natives would be implemented by the end of the year.
The Socialists see economic as well as political distress as the root cause of dissent throughout the empire. The empire is poor and backward. In 1982, it required nearly $2 billion in subsidies, nearly 25 percent more than in 1981.
The economies of most of the territories are fragile, based on tourism and cash crops, such as Guadeloupe's staples of bananas, rum, and sugar. Their combined trade deficits last year ran to some $1.25 billion. Unemployment averages 25 percent and is as high as 33 percent in some places.
''We are trying to help make the territories and departments more productive and independent economically by forming local committees to encourage local investment,'' Mr. Fournet said.
That strategy, though, will take time to pay off. Meanwhile, payments from the mainland continue to increase. The Socialists have integrated the overseas possessions into their expanded social welfare system.
With all the trouble it has from its far-flung ''Falklands,'' why does Paris keep up the expense?
Mr. Fournet leans back and reflectively scans the confines of his spacious office, luxuriously furnished but tattered at the edges in comparison to the normal opulence of French ministries. He sits in the same chair that only a generation ago was occupied by an official in the Ministere des Colonies.
''We don't count every sou that goes to l'Auxerre (a region in Burgundy), so why would we count every sou that goes to Martinique,'' he explained. ''Martinique has been French for nearly 300 years, after all. We are all French.''