Wearing a baggy green coat and carrying a black velvet Beau Brummel hat under his arm, France's former ambassador to the United States, Jacques Kosciusko-Morizet, spent several hours the other day going from shop to shop looking for votes.

Campaigning for a seat in the National Assembly, the 65-year-old Kosciusko is the point man in the Gaullist struggle to mount a comeback in its former stronghold here in the Champagne country of northern France.

The Communists won the city hall here in Reims from the Gaullists in the general French left sweep of last March's municipal elections.

The French left's margin of victory here, however, was thin. If the Gaullists and their center-right allies who have governed France since 1958 are going to hold onto enough seats in the National Assembly elections two weeks away to keep the French left from coming to power, this is one of the seats they must win.

The French governing alliance would seem to stand a good chance here in Reims if the Socialists and Communists fail to agree to restore their unity arrangement before the National Assembly balloting.

Kosciusko-Morizet and his centrist rival endorsed by President Valery Giscard d'Estaing'd party have already agreed to support whichever of the two runs stronger in the four-man race when the run-off elections are held a week later.

They have also agreed to direct most of their fire during the campaign against the left rather than each other.

The centrist is Jean-Louis Schneiter, a 45, a candidate whose local credentials would normally have made him a shoo-in over Kosciusko. Schneiter is a mayor here, and the son of former a champagne broker, a former deputy mayor and prominent national politician, Pierre Schneither.

While many local people seem intrigued by Kosciusko's proposition that as a retired prestigious ambassador he would become the ambassador of Reims and the Champagne region to Paris and the world, he labors under severe handicaps.

He is old, he is unknown locally and he has an unpronounceable name, one observer said. The locals jestingly call him "Cassius Clay" because that is about as close as many can come to pronouncing Kosciusko-Morizet.

As a newcomer, however, he is untarnished by the bitter local quarrels that had much to do with the left's victory here in last spring's municipal elections.

Kosciusko also has one great asset --Gaullist leader Jacques Chirac and his party.

Unlike the Gaullists, the members of Giscard's team have no strong local or national organizations to help them.

Kosciusko has gotten Chirac, former Prime Minister Michel Debre and a procession of Gaullist war heroes to join him on the platform at campaign rallies.

No one else in Reims has campaign literature like Kosciusko's. His slick-paper biographical brochure includes photographs of him with Winston Churchill, with exotically robed delegates at the United Nationa, with Charles De Gaulle, Henry Kissinger, President Carter, Duke Ellington, and finally, drinking champagne from a methuselah -- a champagne bottle eight times the ordinary size.

The normally taciturn ambassador has also learned how to take his cue from the Gaullist national campaign.

Speaking in a cold school auditorium in an outlying part of his district to an audience of champagne makers, Kosciusko was received with polite silence when he talked about tax breaks for champagne: "Champagne is our petroleum. We must export it to pay for the petroleum we must import."

But the audience bubbled into applause when Kosciusko uncorked the law-and-order themes that have flowed throughout Chirac's campaign.

The loudest applause of all came when Kosciusko spoke about the subversion of school children by leftist teachers. "There can be no rotation in government between freedom and slavery," he cried.

Party workers had plastered the hall where the rally was held with what are called Gaullist "oui-non" postters.

"Oui to free France, non to submission."

"Oui to progress, non to stagnation."

"Oui to participation, non to egotism."

The questions from the audience showed that Kosciusko had been largely preaching to the converted. There were no leftist hecklers.

Indeed, Kosciusko seems to have made up his mind not to bother with those who are unlikely to vote for him.

In a walk down one of the main shopping streets of Reims, he entered every door to talk to the shopkeepers, hardly bothering with their younger assistants and almost totally ignoring the young people in the streets and cafes.

The polls show that 18 to 21 year olds, whom Giscard has given the vote, are overwhelmingly leftist.

"The shopkeepers are for me," said Kosciusko as he emerged from a door, adding with a little grin, "Quel metier

What a profession!"

"In a small grocery store, a midleaged woman in a fur coat dropped out of line to approach the Gaullist candidate. She asked him how to cast two proxy votes she had been sent from the Canary Islands.

"That one's three votes," Kosciusko said with a smile as she walked away.