Queen Elizabeth II of Great Britain signed Canada's long-disputed new constitution into law today as protesters demonstrated in Quebec province, home of the French-speaking minority.

The street marches, organized by the Parti Quebecois provincial government, which seeks independence for Quebec, underscored the continuing internal trials Canada faces despite the recent resolution of some tensions between Prime Minister Pierre Trudeau's administration and the country's provincial governors.

Most of the country's native Indian leaders, dissatisfied with rights provisions accorded them under the new governing charter, also refused to participate in the ceremonies today.

Speaking in a rainstorm in front of Canada's Parliament buildings, the queen declared the constitution "truly Canadian at last," but expressed regret that Quebec was boycotting the ceremony.

Although the proclamation will not change Canada's political status, it nonetheless marks an important step in national development. For the first time in the country's 115 years, Canadian elected representatives will possess full power to amend their own constitution. Gone is a situation widely considered an embarrassing reminder of former colonial status.

The British Parliament approved transfer of constitutional authority from Britain, Canada's mother country, last month.

Trudeau told thousands gathered on Parliament Hill that Canada was breaking its final "colonial link" and "at long last acquiring full and complete sovereignty."

Formal proclamation of the new governing charter was carried out by Queen Elizabeth in her dual capacity as sovereign of Britain and of Canada's constitutional monarchy.

The Constitution Act, 1982, which will henceforth serve as the country's basic law, includes a wide-ranging bill of religious, linguistic and democratic rights that adds constitutional validity to Canada's traditional civil liberties.

Since 1931, when it obtained full sovereignty from Britain, Canada has had the power to take charge of its own constitutional affairs. But doing so was always thwarted by the failure of Canadian leaders to agree on how power should be shared. The prolonged dispute, usually pitting the central government in Ottawa against the premiers of Canada's 10 powerful provinces, was fought over the same states' rights issues that have been debated in the United States.

This failure to "bring the constitution home" symbolized the country's helplessness, in the face of wrenching regional and cultural differences and conflicting interests, to give cohesion and purpose to its federal system.

After years of talks, Trudeau produced a compromise last fall with the premiers of the nine English-speaking provinces, paving the way for approval by the Canadian and British parliaments of a new constitutional package.

But Trudeau's political triumph, although fulfilling one of the foremost goals of his 13 years in office, was far from complete. The government of Quebec, home of Canada's French-speaking minority, refused to join the pact, dashing Trudeau's deeply held aspiration, as a French Canadian, to allay nationalistic sentiments in Quebec that have long threatened to split up the country.

In a province-wide television address shortly after the queen's arrival in Canada Thursday, Quebec's proseparatist Premier Rene Levesque issued an impassioned plea for independence. Levesque, who claims the new constitution reduces his province's power to control its cultural and economic destiny, said the statute is "totally unacceptable." Quebecers, he warned, should "decide soon, before it is too late, that Quebec must belong to us."

By isolating that province, the constitutional compromise reopened with all its divisive force the most troublesome of issues here--the fundamental "Canadian question" of how French and English can exist side by side in one nation. Moreover, while Quebec commands most urgent attention, there is little doubt that the events of today will usher in a period of broad political and judicial uncertainty likely to strain the country's uncertain unity further.

Clashes over control of Canada's plentiful resources will likely continue to frustrate efforts toward regional cooperation. All signs point to more squabbles between the Trudeau government and oil-rich Alberta, the most prosperous of Canada's western provinces. The focus will be on such issues as resource taxation and the joint financial incentives needed to spur development of massive synthetic oil plants in the Canadian north.

Dissatisfaction among westerners, similar to the "Sagebrush Rebellion" in the United States, also is mounting, fueled by a deep-seated conviction that they have been traditionally shortchanged economically to the benefit of populous Quebec and Ontario. This sentiment has been inflamed by Trudeau's nationalistic energy programs, which have contributed to falling oil-company profits and an exodus of drilling rigs to the United States.

A western movement to secede from Canada is flexing new muscles. In Alberta, the western independence party may seriously challenge Conservative leader Peter Lougheed, arguably the country's most powerful provincial premier, in the next election.

A struggle over resource jurisdiction also is boiling between the Trudeau administration and the East Coast island province of Newfoundland, stalling development of Canada's most promising Atlantic offshore oilfield.

All of these provincial strains heighten the current widespread sense of anxiety and pessimism among Canadians, something the appearance of Queen Elizabeth, for all her popularity, is unlikely to dispel. With unemployment at 9 percent and inflation at 11.6 percent, Trudeau's popularity plunged to its lowest level in three years in the most recent Gallup Poll. Even in his own Liberal Party, people are growing impatient for Trudeau's resignation, and his constitutional success may provide the opportunity.

The aftermath of this reform process also will see an upheaval in the Canadian judicial system as courts are asked to interpret the wording of the new bill of rights. This represents a major departure with past practice, under which the country's legislative bodies functioned as the ultimate judge of rights issues.

Important questions about the future of Canada's native Indians, particularly their land claims based on British treaties, were also left undecided, with federal and provincial governments committed to another constitutional conference within a year to discuss them.