An intense and often chaotic campaign for the first mayor Paris has elected in a century came to halt yesterday with the outcome apparently riding on a duel between two strongwilled women battling in the French capital's largest electoral district.

About 33 million voters are expected to go to the polls Sunday to elect city councilmen and mayors in a total of 36,000 towns across the country. The elections have taken extraoridinary importance this year because of the growing struggle between the ruling conservative parties and their leftist opponents for controal of France.

With the Socialist-Communist coalition appearing to gain strenght, Sunday's first round of municipal elections has become in effect a primary pitting President Valery Giscard D'Estaing's reformist coalition against the more conservative Gaullist Party headed by former Prime Minister Jacques Chirac.

The Paris results will point the way toward a continuation of Giscard's mild reform program or a retrenchment into the more aggressively anti-Communist, status quo outlook of the Gaullists.

The frontrunner on the conservative side will not only confront the leading leftist candidate in the March 20 runoff balloting but will also be in a position to call the tune in determining a strategy to use against the Socialist and Communists in the elections for a new Parliament to be held within a year.

The campaign for Paris mayor between chirac and Giscard's appointed candidate, Industry Minister Michel d'Ornano, has been close and acrimonius. Public opinion polls show only a percentage point or two dividing the two men in most of Paris' 18 voting district, which will choose 109 city councilmen who then elect the mayor from their ranks.

Nowhere is campaign tension higher than in the populous 15th Arrondissement, or District in Paris, where Giscard's minister of culture, Francoise Giroud, is challenging Gauldist Nicole de Hauteclocque, who has served as council present.

Giroud, diminutive, steel-and-velvet woman, became Giscard's minister of culture last year after serving as the head of the government's Department of Women's Affairs and a long career as the most important woman in French magazine publishing.

A victory for the ticket she heads in the 15th Arrondisement is likely not only to propel D'Ornano to a narrow lead over chirac, who would then throw his support to D'Ornano in the second round, but also to give Giroud and her reformistr Radical Party new influence in the government.

The Gaullists themselves have underscored the threa that the low-key, unorthodox campaign Giroud has been wagin in schools and meeting halls across the district evidently represents to their position. They shifted their fire from D'Ornano this week to the 59-year-old culture minister.

A Gaullist parliamentarian demanded a judical investigation of the claim on Giround's campaign literature that she had received the Medal de la Resistance, a World War II decoration awarded to about 70,000 persons for "acts of faith and courage" in the underground struggle against the Nazis.

Giroud launched an immediate and vigorous counterattack against "these base charges." She went on television to concede that the medal was not listed in the official register, but produced testimony from well-known resistance fighters about her activities in occupied France, her brief imprisonment in a Gestapo-run prison and the recommendations that she be given the medal. They pointed out that her sister, deported to a concentration camp, had also received the decoration.

The issue of the model itself would appear to be of no great consequence to an increasingly younger electorate. But Giroud's decision to feature it in a campaign against the political heirs of Charles De Gaulle revived questions about the wisdom of the campaign she had undertaken.

If she wins, she will eliminate De Hauteclocque from the council. De Hauteclocque's seniority on the council makes her one of the most important women in French local politics.

Giroud has frequency come under attack from militant feminists here for not showing solidarity with the feminist cause. She herself has little to say today about what she was able to accomplish while heading the ministerial-level Department of Women's Affairs, a post that was simply done away with when Giscard shifted her to culture.

This is the first time that she has run for elected office - she heads a list of 11 City Council candidates running under the D'Ornano banner - and she admits that she is doing it only because Giscard asked her to.

Frequently masking behing an engaging smile the combative nature that has helped her struggle to the top in a female Horatio Alger story, she avoids the standard speeches made by other candidates at campaign meetings. She asks, in a low voice, individual members of the audience what is on their minds. She listens, and if an opening presents itself gets in a plug for Giscard's record and D'Ornano's promises.

Her father dead, she began working as a secretary at age 14 and became a movie script girl at 17. Entering journalism at the end of World War II, Giroud quickly became the editor of the woman's fashion magazine Elle and then moved on to help Jean-Jacques Servan-Schreiber start France's first newsweekly, L'Express, in 1953. The two also took leading roles in the Radical Party.

She left magazine to join Giscard's government in 1974, but she still maintains ties to it. A flattering cover story on her in this week's L'Express features photographs of her addressing Giscard and playing cards at home in the 15th Arrondissement with her graandson. The magazine ignores her opponent.

"I have had luck." Giround once told an interviewer who asked about her rise. "And I have seized it when it passed by."