Paris — Paris has switched from carrot to stick in trying to quell Corsican nationalism. Faced with defiance and violence from the Corsican National Liberation Front, President Francois Mitterrand has put aside his earlier conciliation. Instead, he has responded to the threats, shootings, and bombings of recent days by:
* Formally outlawing the Corsican liberation movement, making membership in the group a crime.
* Sending mainland police officers to crack down on separatist violence.
* Appointing the renowned Robert Broussard - currently head of an elite Paris-based anti-gang brigade - to the powerful post of commissioner of the republic to oversee the Corsican operation.
''The law of the republic will be enforced,'' President Mitterrand told the nation. Officers from the mainland were named to replace the police chief of the island's capital, Ajaccio, and the head of the local police intelligence. At least 12 other mainland police were also sent to the island.
All France's major political groups have applauded the measures taken on Corsica, the Mediterranean island where Napoleon was born. The reaction among Corsica's political leaders has been largely favorable as well. And many Corsicans, a large majority if one believes last summer's election results, support strong ties with the mainland.
Still, Mr. Broussard will have a hard time wiping out Corsican terrorism. Although reports say the liberation front has only a few hundred members and 50 or so active guerrillas, they add that Libya may be providing their arms and that training may have come from Palestinians in Lebanon.
The separatists also undoubtably have some local support. Many Corsicans, especially the young, bridle at what they consider the French ''colonization'' of the island. This sentiment has been strengthened in recent years as the island has been transformed by tourism and large-scale agriculture - activities largely controlled by mainlanders.
Add the traditional law of silence - ''omerta'' - to this equation and the result, police say, is a population that is largely uncooperative with law enforcement officials.
The latest trouble flared up just before New Year's. The separatists announced that island residents from the mainland would be forced to pay ''a revolutionary tax'' of 3,000 francs ($450) a month. A veterinarian, Jean-Paul Lafay, told reporters he would not pay. The next day a masked man shot him three times, seriously wounding him. In addition, the homes of two other men who refused to pay were bombed.
The Mitterrand government took the tax declaration as a direct challenge to its authority. Although Dr. Lafay survived the attack, it was considered particularly serious because it was the first time the separatists had drawn blood since the Socialists' May 1981 election. And it was the first time they had tried to kill a civilian since the beginning of their violent liberation campaign in 1976.
When Mr. Mitterrand came to power in 1981, the separatists declared a truce, hoping that he would meet their demands. The new President responded by adopting a conciliatory attitude, granting amnesty to some, and sponsoring last summer's elections, which gave Corsicans considerable control over their local affairs.
Moderate autonomists took part in the elections. But the hard-liners of the liberation front boycotted them, saying the local assembly would not have Enough power. During the weeks preceding the early August vote, they renewed their bombings, though fastidiously making sure the explosions caused little damage.
Despite the violence, the elections went off on schedule. A large turnout seemed to approve continued strong ties with France. ''Corsicans have ratified the autonomy plan,'' beamed the minister for Corsican affairs, Bastien Leccia, in a post-election interview with the Monitor. ''We have succeeded in defusing the bombs.''
But the local assembly soon found itself helplessly deadlocked, and the separatists decided the time was ripe to act. Their latest, more violent attacks have ended Mr. Mitterrand's attempt to soothe their feelings. Now he seems to be out to crush them.