Well, Chrétien had prepared a speech in case of defeat in which he said the vote was legally merely consultative, and the margin of victory too narrow to be recognized. Civil war is a non issue, though, quite obviously, this just isnt the canadian mindset at all. But you would see attempts by Ottawa to deny the results of the vote.
Quebec is however well prepared. France will recognize Quebec's independence within hours, if not minutes, of the official announcement. Billions of Quebec`s dollars are available at the Premier's order to prevent any faltering of the currency. Of course, Quebec's Office of Foreign relations assumes the mantle of Foreign Ministry immediately. The delegate to the United Nations is already chosen, and present at the UN's seat to announce the entrance of Quebec in the community of nations. The Republic's transitionary commitee has a well prepared agenda of negociations, to debate points like the share of the federal debt that belongs to Quebec (Between 21,4 and 23.7%, depending if you base yourself on population, or GNP percentile), economic arrangements if any (Though Ottawa would like to say no, a million jobs just in ontario depend on Quebec. You cant exactly just severe those kind of ties just like that), and the various other things.
These things above are all based on OTL's plans on both sides for the transition. Canada would try to stall and reject points, arguing based on the constitution (Though Quebec never signed it). They would even probably suggest that the regions who primarly voted no be given a choice to remain Canadian, but this would never happen without military agression, because the boundaries of the provinces are well determined, and of course, these very regions were part of the "no" voters in the first place. Quebec has however the big ace in its sleeve, the fact that it democratically chose to secede and succeded despite all attempts to sink the boat. Most nations of the western world would therefore have no choice but to accept that. Some eagerly, some based on self-interests, others because there are few other options.
The somewhat volatile character of the prime minister of Quebec is to be taken into account at this point. He swore many times privately, and publicly later on, that he would have proclaimed independence unilaterally if negociations did not give satisfying results between 24 and 72 hours following the end of the polls, and I am certain he would be true to his word. Canada would take offense at that action, for sure, and would threaten economic sanctions, but the act would be done. Europeans would be the firsts to recognize Quebec. This is where it gets interesting.
There were three copies of the French plans for recognition of Quebec. The first, the best case scenario, was a plain recognition, offering friendship, trade and political assistance to the new kin-country on the other side of the atlantic. The second, in the scenario where Ottawa pushed hard for partitions of english areas, included a guarantee of teritorial integrity and inviolability and a promise of assistance against attempts to break this integrity. The last, the worse case scenario, in the strange event where hotheads would prevail to the point where some people wished military action to prevent secession - offered simultanously an immediate guarantee of independence, asked formally the UN to condemn any attempt at violating the soil of the Quebec, and offered to dispatch immediately French military units to assist the fledging army of the native republic.
Now, these were contingency plans and its unlikely the third scenario could ever happen, but i was mentioning anyway. It does show that Chirac's commitment to the new republic was quite strong. The disclosure of these plans afterwards substantially cooled relations between France and Canada afterwards in OTL, up to until 1999 or so.
So, assuming things go the average way, negociations makes slow progress, Quebec declares independence, Canada refuses to recognize it right away, but most of the rest of the world does, the US stays more quiet for a few days, Quebec says a flat no to any partition plans, France backs it to the hilt, trade is disturbed for several days, Ottawa begins to speak about keeping the rest of the country together, and when it becomes obvious that this is a fait-accompli, the USA recognizes the republic. Ottawa then tries to object to Quebec's joining of NAFTA and other organizations they feel entitled to participate in, and set up tariffs on areas that favors them.
The next few months are of course more politically active than usual in Quebec. The Prime Minister becomes the first President of the Republic and the foreign ministry works on all levels to break diplomatic isolation and resume trade to pre-independence levels, mainly through joining NAFTA. The first North american breakthrough is obtained two weeks later when the USA considers all economic treaties in existance with Canada now applies to Quebec as well, until further notice, aside from the thorny issue of the NAFTA seat.
In Canada, several parties believe that Quebec's secession invalidate altogether the Confederation of 1867 and that another union must be formed. Ottawa strongly objects this point of view, and is struggling on all sides to keep the country in one bloc. Economically, pressure mounts rapidly in Ontario and the Maritimes where tariffs imposed on and by Quebec are hurting the economy seriously. Negociations starts again behind the seat, on the basis of the fait-accompli.
In Quebec, though there is atfirst a small wave of initial emigration of english citizens, and some concerns amongst the first nations (the natives), the situation on that level returns to calm shortly after. Buisnesses and banks, obviously, stay where they are. There is a myth that many would like to leave an independent Quebec, but its a mystery why money-making oriented buisnesses who find Quebec quite profitable, would wish to leave it... while they are busily spending capital to establish themselves in Saudi Arabia, Eastern Europe and China in the meantime.
It takes almost three years for the situation to stabilize fully everywhere. Though it has to make many concessions, Ottawa manages for a time to keep the rest of country together. By 1997, Quebec's independence is fully recognized, and their place in the various political and economic structures are secured. Quebec - more leftist and pacific than most of Canada - choose to stay out of NATO and establish in its constitution provisions akin to those found in Switzerland's. Armed forces are minimal and purely defensive, and any legislation related to war issues requires the unanimity of the National Assembly, and the President's veto.
Quebec also demonstrates its ability to adminster its country quite well, scoring a series of easily balanced budgets, thanks to the taxes reapatriated from Ottawa. Trade bilans are excellent, and social structures prooves to work quite well. Of course, for the average citizen, after the big thrill of the first "free" year, its back to buisness as usual both in Quebec and Canada. There are frankly few other plausible outcomes aside from this.
As for the changes upon the world? Well Quebec never wished to have a crucial impact in world affairs. Though culturally and economically quite open, the nation would most likely remain focused quite inwards politically, and the relief of the Quebec-Ottawa bickering would be very welcome. Life in the US, Europe, or in England, would be for all practical purposes, unchanged.
Later on, Quebec would generally take a European stance on US foreign policy following 9-11. Careful support for the war in afganhisthan (though its fully out of question to dispatch any troops or assistance there), and a firmly opposed stance (akin to France's) against the Iraqi aventure.
In internal policy, the Parti Québécois would probably not last too long, having accomplished the goal that kept it together. The Liberal party would also not last in its current shape, too closely kept together and funded by English canada. Possibly an ADQ takeover in the 2003 elections. Its as much as a center-party Quebec can possibly accept, and they would probably be a bit more mellow in their critics of the campaign of Iraq.
Opinion polls in 2004 shows the western provinces have support rates up to 44% for independence, and 31% of Saskatchewan declares it would not be opposed to joining the USA.