How close did Quebec come to leaving Canada in the 1995 referendum?

Very close. On 30 October 1995 Quebecers voted on whether Quebec should become sovereign, and the No side won by 54,288 votes, with 50.58 percent of the votes cast. Turnout was 93.52 percent, the largest in Quebec's history and higher than at any provincial or federal election in Canadian history.

It was the second such vote. After the Parti Québécois won power in 1976, it held a referendum in 1980 seeking a mandate to negotiate "sovereignty-association" with Canada, and that was decisively defeated, with 59.6 percent voting no. In 1995 the early predictions were again of a heavy sovereignist defeat. Then the Yes side flourished after Bloc Québécois leader Lucien Bouchard took it over.

The question itself was long: it asked whether Quebec should become sovereign, after having made a formal offer to Canada for a new economic and political partnership. Voters split sharply. Yes was the choice of French speakers by an estimated majority of about 60 percent, while anglophones and allophones, people whose first language is neither English nor French, voted No by a margin of 95 percent. The closest result in any riding was in Vimont, in Laval, which Yes won by 6 votes.

What would a Yes have meant? The two sides disagreed. Sovereignists believed that 50 percent plus one vote was binding. The No campaign head, Daniel Johnson, disputed that a simple majority was enough. After the close result, the federal government referred the issue to the Supreme Court of Canada, which stated that the unilateral secession contemplated in the referendum was illegal.