The strongest party in Quebec that had not participated in the declaration of independence was the Communist Party of Quebec. To attempt to appease Communist demands, the Quebecan Constitution was massively amended to allow for a Marxist state to some level, and Catholicism was disestablished. This did gain some Communist support, but that was offset by an exodus of Nationalists and Conservatives to the Canadian side.
The People's Republic only had tenuous control over Quebec City and points east, and its very limited power base was in the Ungava Peninsula. Massive redistribution of wealth occurred in areas under its control, and several First Nations tribes were forcibly integrated into Quebecois Society. Many of these policies were reversed, though some have said that the breaking up of the estates, some of which remained broken up, have contributed to Quebec's rapid economic recovery following the war, though others say that it is the massive aid that is still coming from the United Kingdom.
Effects on the War
The Communists hated the Kingdom of New England, as it combined their traditional disagreement with monarchy and the suppression of Vermont. Therefore, Quebec units were ordered to attack their former allies, resulting in the confusion at the Battle of Boston.
After the War
The People's Republic ruined the cause of Quebec independence. The suppression of Catholicism and others hurt the idea of an independent Quebec for the following years, and the idea is seen as all but dead by the public.