Left, right battle within Canada's Conservatives

The heaviest political fighting in Canada is not between two opposing parties but within the ranks of the Conservatives. The left and right wings of the Progressive Conservative Party are battling for the leadership. And it appears likely that the party will make a sharp move to the right during its leadership convention next month.

The only thing that would prevent that is if party leader Joe Clark, who is on the left end of the party spectrum, keeps his job. That could still happen, but Mr. Clark's early lead is slipping. There is talk that if he looks a winner on the night of the convention, the party's other leading candidates will mass their support to make sure Clark does not get his old job as prime minister back.

Clark has already served as prime minister. The Conservatives won an election in June of 1979, lost a vote of confidence in December, and were back in the opposition facing Prime Minister Pierre Trudeau by February of 1980. In large measure Clark's loss of the vote of confidence that forced the election stemmed from his own failure to line up support.

There are a lot of delegates who will support Mr. Clark's second bid for the office - he has been working hard to make sure of that. But there are also a lot of Conservative Party supporters who resent his having let power slip from his hands.

British parliamentary tradition says that when a leader botches it, he should quit. Mr. Clark has preferred to stay on.

The leadership campaign was forced on him earlier this year when he received less than 70 percent of the vote of confidence at the annual convention. He did not have to step down; he just decided that less than 70 percent was not enough support. Now he and six other men are running for party leadership. With more than 52 percent of the general electorate favoring the Conservatives in the polls, the man who becomes Tory leader is likely to become the next prime minister when an election is held in a year or two.

For years the Progressive Conservative Party has been dominated by the progressive side. Mr. Clark and his predecessor, Robert Stanfield, both stood for slightly left-leaning social programs.

The only right-leaning party member to serve as prime minister in the past five decades was John Diefenbaker. He was a Tory of the old school, fiercely pro-British, suspicious of the Americans but a fighter for the rights of the little guy.

The big guys did not like him. The Liberals became the party of big business, the home of the sophisticated. The Conservatives became a party of western Canada, small business, and the alienated who believed in the old ''Canadian'' values.

The Liberals are the party of central Canada, and their power base is in the industrial provinces of Ontario and Quebec. They have all but one of the 74 federal seats in Quebec. It is partly because the Conservatives have traditionally been seen as a party of the British Empire that they did not get any support in Quebec.

The Tories have never had a French-speaking leader. Although Mr. Clark speaks French, he does not do it flawlessly. And in an effort to court French votes, he has been ''soft on separatism,'' according to his opponents. The separatist Quebec premier, Rene Levesque, has endorsed Mr. Clark, saying he is open-minded. That endorsement may work against Clark. His main opponent, Brian Mulroney, says he ''will not play footsie'' with the separatists.

Among those running for leadership of the party, Mr. Clark and David Crombie are the only men who could be described as left-of-center. The rest are to the right - all the way to Toronto member of Parliament John Gamble, who is on the extreme right and is given to making anti-French remarks in his campaign speeches.

The rank and file of the party has turned strongly to the right, and it appears certain that after the June convention the leader and the party will be more right wing. And so, probably, will the next government of Canada.