I think that question should be differently formulated, as I don't think you can reduct the Quebec engagement as a question only between them and France. The relations they have with the United Kingdom at the moment are maybe more important to their non-engagement than the small ties they still keep up with France.

First, Canada did not choose its participation in the first World War. As a dominion of the United Kingdom, they have to join them when the war is declared in August 1914. What they can choose howewer, is how many men they will send, and the equipment they will carry with them.

The first call to volunteers is made right after the declaration and two months after the first Canadian corps is ready. But « the Official sources show that French-Canadians represent less than 3.5% of the first contingent, so 1245 volunteers out of 36267 » (Béatrice Richard, [1] – Nicholson [2]). In fact, 70% of enrolled are recent immigrants from the Britannic islands.

According to Richard, there are multiple reasons to this low number. First there is almost no ties with France since the cession to England in 1763, and the French-Canadian people don't see France as the « motherland » anymore, thus they don't feel that bond the English immigrants had with the throne.

Secondly, they didn't think either that they owed something to the Crown. They knew they were traded after the defeat and still felt a bit under « occupation ». Furthermore, remember that in the early 20th century, english is the only language in the army, and very few Canadian-French speak it, so they can't understand orders from their superiors. And in 1914 there wasn't a specific french bataillon, they were dispatched in english-speaking units where they had a rough time to acclimate. It made the volunteering a lot harder despite a big recruting campaing (Marcelle-Cinq Mars, [3] – Carl Pépin [4]).

Thirdly, the Quebec was a rural province, and a lot a men simply didn't engage because of the upcoming winter, as they didn't want to abandon their farms and families.

Then, in 1916, the Canadian government adopts the conscription. The Prime Minister Robert Borden says the country will send 500 thousand people overseas. 18,827 French-Canadian don't present, and it could be seen as a special reluctance to to go war, but the number is high in every canadian province.

At that time the Canada already suffered 30,000 casualties in Europe, in a country of 7 million people only, and a lot of people tried their best to get exempt, and disappeared in the nature when they could not get an official exemption. There was also only one French unit in the whole army, which may have had consequences on the Quebecers desertions (Carl Pépin, [4]).

To conclude, i don't think their resistance was against France, but more against fighting in Europe in a somewhat foreign army.

(but maybe i'm a bit too far away from the original question)

[1] Béatrice Richard (Royal Military College of Saint-Jean the Richelieu) ; Colloque « Mobilization, tensions, refusals in 1914-1918, Quebec during the War » ; Paris ; 2014

[2] Nicholson G.W.L ; The Canadian Expeditionary Corps, 1914-1919 : Official History of the Canadian Participation to the First World war ; Ministry of Canadian Defense ; Ottawa ; 1963

[2] Marcelle-Cinq Mars (Library and Archives Canada) ; Colloque « Mobilization, tensions, refusals in 1914-1918, Quebec during the War » ; Paris ; 2014

[3] Carl Pépin (University of Montreal) ; PhD « The relations between France and Quebec during the First World war » ; Montreal ; 2008

I've heard it claimed that one of the contentions for Quebecers was that a lot of them were Bourbon monarchists and they didn't see the French Republic as legitimate, is there any truth to that?