PARIS -- The rumor that did the rounds at the European Community's recent summit in Birmingham sounded so plausible that even the venerable BBC fell for it. President Francois Mitterrand of France just turned 76 and recovering from prostate surgery, had supposedly collapsed over lunch and had to be carried out -- or so the story went. The French denials came swiftly, and the issue was laid to rest when Mitterrand himself emerged pale but still kicking to talk to the press. With a touch of black humor, he joked about his "rapid resurrection".


Even so, the issue of Mitterrand's health is starting to have a domestic political impact.


France is now engaged in the sort of death-watch speculation that characterized the final days of Leonid Brezhnev and the brief reign of his two successors, Yury Andropov and Konstantin Chernenko. But unlike in the former Soviet Union, where a successor was chosen behind closed doors, the gossip about Mitterrand has touched off a very public battle in France that borders on the grotesque.


Both leaders of France's two rightist opposition parties, Jacques Chirac and Valery Giscard d'Estaing, are bickering furiously as each tries to present himself as the best choice to be the next French leader. Giscard, who has already served one term as president from 1974-81, suggested on television the other day that he may want to stand for re-election. Chirac, the Gaullist mayor of Paris, had earlier staked his claim to become the next French prime minister, with a clear eye on boosting his chances to become the next president.


All this strikes the French public as, well, rather premature. Legislative elections are due to held in March, but the next presidential election isn't scheduled until 1995. and the unseemly power grab by both Chirac and Giscard, both of whom have been on the French political scene for decades, has provoked cries of anguish and astonishment among their own following.


People in both parties are aghast at the damage the squabbling between the two men, who can't stand each other, is doing to their national standing. Many on the right believe the time has come for both men to step down and make way for a new generation of younger leaders.


To end the feud, the two factions have revived the idea of holding U. S. -style primary elections to pick candidates. But that in itself has sparked a new round of nasty polemics, and provided plenty of ammunition to French editorial writers and satirists. At the president's Elysee Palace, officials can barely contain their glee. Mitterrand may be suffering a little from radiation treatment for his cancerous prostate, they say, but he is greatly amused by the public self-destruction of his political opponents.