THE ABRUPT resignation of Quebec's premier, Rene Levesque, marks the end of a turbulent chapter in Quebec's and Canada's history. Ostensibly, Mr. Levesque leaves office under a political cloud. His Parti Quebecois trails the opposition Liberals by more than 2-1 in the polls and seems sure to lose the next provincial election. The party is split between those who agree with Mr. Levesque's emphasis on economic issues and those who want to fight the next election on the issue of separatism from the rest of Canada. There is no doubt that the party has failed in its purpose of separating mostly French-speaking Quebec from mostly English-speaking Canada.

Yet in another sense Mr. Levesque and his movement have been successful. They have resolved, though at some cost, a difficult problem that deeply affects the daily lives and prospects of some 6 million residents of Quebec. The problem is language, and it came to the fore in the 1960s. Quebec's majority of French-speakers, part of a tradition-bound rural society, educated only scantily in church schools, suddenly was receiving the education and training needed to get ahead in industrial North America. But in the big office buildings of Montreal all important business was conducted in English.

Mr. Levesque's party came to power in 1976 and passed a series of laws requiring the use of French in everyday life. This was costly: many businesses left Montreal for Toronto. It was often unfair to individuals. Yet it did promote the use of French and open up opportunities to those whose main or only language was French.

Mr. Levesque was less successful in his goal of achieving separation of Quebec from Canada. His 1980 referendum calling for some form of independence was rejected not only by the English-speaking minority but also by the French-speaking majority in Quebec. In a recent poll only 4 percent of Quebec respondents favored independence.

The road for the Parti Quebecois has been mostly downhill since. But it has been the victim just as much of its success as of its failures. The problem that it and Canada's federal government have been grappling with is not likely to recur. Economically, if not linguistically, Quebec is part of industrial North America. Politically, Quebec is firmly, if still a bit uncomfortably, part of Canada. That's a solution and, given the passions and the violence that attended the politics of separatism, one of the better ones that could have been imagined not too long ago.