When Claude Lamblin took over last year as the first Communist mayor of Reims, the 40-year-old school teacher's future could hardly have looked brighter.

The French left had just won control of two-thirds of France's largest cities, and led by candidates like Lamblin, the Socialist-Communist coalition appeared to stand a good chance of emerging victorious in the 1978 National Assembly election now only two weeks away.

But a year of bitter feuding - on the local level as well as the national - has put the outlook for Lamblin and the French left very much in doubt.

While Lamblin remains personally popular, he suffers from having presided for a year over a city administration paralyzed by constant bickering between Socialists and Communists.

Things have gotten so bad between the Socialists and Communists here in Reims that when the muncipality changed a street name to Rue Salvador Allende, in honor of the late Chilean president, the Socialists and Communists will agree at the last minute to reinslate their joint unity agreement that has served them well in elections in recent years.

If they do paper over their feud, either Lamblin or the Socialist candidate in this destrict, Georges Colin, would withdraw after the first round pf voting for the National Assembly, and throw his support to whichever of the two ran stronger in the four-man field.

In that event, the leftist candidate would stand a much better chance of defeating the Gaullist or Centrist candidates.

Sated in his ornate wood-paneled office last week, Lamblin made it plain that he would only go along with this if an agreement to reinstate the Socialist-Communist joint arrangement was struck at the national level.

Lamblin came to power because of a Socialist-Communist agreement to sponor a joint list that gauge each party 18 seats in the Reims municipal council.

The Socialist conceded the mayor's spot to Lamblin before the election because the Communists had an electorial lead in the previous legislative elections.

For all their joint arrangement, however, the Socialists compalin today that they have largely frozen out of city affairs.

At the first municipal council meetings after the Socialist and Communist parties formally split nationally in late September, the local Socialists voted against Lamblin's supplementary budget request, turning local guerrilla skirmishing into open political war.

The Socialists accused the Communists of hounding a town hall usher into resigning because he refused to join the Communist Party, and of hiring a cousin of the mayor as a cultural affairs officer.

The Communists accused the Socialists, who control the Greater Reims District government, of voting themselves huge retroactive salary in creases.

The Socialists also say the Communists have stuffed the city government with their own people. Independent observers, however, say that apart from the appointment of four Communists that caused an outcry in the first days of the Lamblin administration, the Communists have taken care to appoint only the most qualified applicants regardless of party.

The Communists did not bring in more new people than any new administration does after taking over. In fact, Lamblin even kept the old mayor's confidential secretary.

The people the Communists did bring in are more active and dedicated than most. Lamblin said that by dividing his mayor's salary of $1,700 a month among four elected Communist deputy mayors who get paid only $300 to $400 a month each, he has made it possible for them to work fulltime at city hall. Because of the low pay, the Socialists have only one deputy mayor on the job fulltime.

he Communist employes do seem more politicized. Open on the clutered work table of a young woman who works for the mayor was a copy of the Communist Party's book-length proposal for an updated joint national government program, which the Socialists have rejected.

The Communist city government and the Socialist district government, headed by the 47-year-old Colin, seem to spend a great deal of their time trying to make life difficult for each other, to the great discomfort of the civil servants caught in between.

They are currently feuding because the socialists have blocked a Communist proposal for a large central city parking facility.

The Social-Communist relations in the region illustrate why the Communists have been unable to provoke a split inside the Socialist Party despite the presence inside it of a large, organized leftist faction that is almost as suspicious as the Communists are of the traditional Socialist leadership's rightist tendencies.

Most of the top Socialists in the Champagne region, starting with the bearded, bespectacled Colin, former dean of the Reims University Faculty of Letters, are openly proclaimed members of the leftist faction.

As competitors of the Communists for the same working-class vote, they have would up having even worse relations with them than their more conservative Socialist comrades.

The Communist administration has the Socialists have blocked a Commu-relations with them than their more careful not to upset the general citizenry. The Communists voted without question for the usual city subsidies to local Catholic schools.

Asked if he intends to rebaptize other streets besides the Rue Allende with revolutionary names, lamblin recoiled in mock horror.

"Haven't you heard that Stalin is dead? Ideology via street names is dead. It's just a nuisance to the residents and shopkeepers," he said. "They have to change their stationery and tell all their friends and relatives."

Sporting a dark brown shirt, orange tie and a checked tweed jacket, Lamblin criticized and the 20-year administration of his Gaulist predecessor, Jean Taittinger, for having sacrificed the welfare of the local workers to the construction of "prestige projects."

Taittinger, member of one of the great champagne-making families of Reims, had a direct line to the late President Charles de Gaulle, and did not hesitate to use it. He got so many things built for the city that the new leftist administration is having trouble thinking up new projects.

The leftists criticize as a prestige project the east-west highway that Taittinger got the government to build to link Reims with Paris and Alsace-Lorraine, but when pressed to say what he wants done, Lamblin replied that the city needs a north-south highway as well.

Ironically, some of Taittinger's ahievements helped pave the way for the leftists. He brought new industry to the city and built the new satellite twon of Croix Rouge to house working-class families, a population of 60,000 that votes predominantly leftist. Mayor Lamblin lives there.

Where Taitinger's administration concentrated on circuses, Lamblin had focused on bread. Public transportation was made free for the unemployed. School lunch prices were reduced. Special advantages for old people were enacted.

Taittinger's distant style was also scrapped. The Lamblin administration boasts that it has interviewed 3,000 townspeople about their individual problems.

But little has been done to [WORD ILLEGIBLE] with such basic problems as unemployment.

The municipality has deliberately refrained from starting any self-help projects that would sop up some of the joblessness. Lamblin says that the job of the central government Paris.

"Why should the local taxpayer tighten their belts?Let the rich pay he says," he says."Then there would be plenty of work for everyone."