Some background on the subject off the top of my head.
In 1911 when the Conservative Government led by Robert Borden took power in Canada, the South African war "hero" Sir Sam Hughes was installed as the Minister of the Militia, our equivalent of an army department of government at the time. Hughes was famous as part of the Orangist lobby in Ontario, a very boisterous group that was pro-military, pro-imperialist, protestant, pro-Canadian, and anti-Quebec. Hughes was a big fan of personal patronage which was common Canadian governmental practice at the time, so he used his office to exclude and limit the influence of French-Canadians in the Canadian Militia, which naturally led to a decline in enrollment in French-Canadian Militia regiments, which if i remember correctly had similar enrollment as the rest of Canada prior to that time.
When the First World War began, the war was initially popular in Quebec, with future war critic Henri Bourassa calling for Canadian support for the Entente. However this enthusiasm quickly faded over time as French-Canadians generally took a Canadian-centric isolationist viewpoint to foreign affairs. Furthermore, French Canadian Nationalists saw the "Prussians of Ontario" (the Orangist lobby) as a greater threat to themselves then the Germans.
The mobilization of Canadian Volunteers for service overseas was undertaken in a haphazard improvised manner due to the ego and micromanagement of Sam Hughes, which allowed him to determine the makeup and command of his war-raised numbered battalions. This meant that Sam Hughes could block the promotion of French-Canadian Officers, and the formation or call up of specifically French-speaking militia regiments and battalions.
The lack of regiments early on meant that French Canadian volunteers were forced to serve in regiments that were primarily English-speaking and Protestant, causing communication problems. These early difficulties combined with increased antipathy towards the war in later years meant that after Sam Hughes was replaced in 1916, the Canadian government had difficulty in recruiting to keep any French-Canadian Regiment, outside the the famous 22nd (the Van Doos), at any reasonable level of strength. Inevitably most of the under strength French-Canadian regiments were broken up to supply the 22nd.
It is important to note that while Quebec was vilified as lacking enthusiasm for the war as well as for having tepid volunteer enlistments, they were not unique in that regard as many Western farmers had a similar attitude about conscription and the war. The overwhelming number of volunteers came from English speaking cities as well as recent British Immigrants, meaning that the Canadian Expeditionary Force was an English-speaking army outside of the one regiment, and I'm not sure bilingualism was overly common outside of a few specific urban centres such as Montreal and Ottawa.
World War Two was different because the Canadian Government specifically went out of it's way to provide a more Nationwide appeal for volunteers, as well as being more delicate about the issue of conscription. World War 2 was more popular in Quebec then World War 1 was, but still not overly popular.
Their were several French-speaking battalions serving in the Canadian Army in the First through Third Infantry Divisions, all serving with distinction. Additionally their was a French-Canadian squadron in the Royal Canadian Airforce. Their was plans for a greater French presence but their was a distinct lack of Staff Officers which prevented it. All of these French Canadian formations served alongside English-speaking battalions, but I don't recall seeing any specific mention of language barriers or difficulties in the historiography that I have read, though their undoubtedly were some.
Overall though the Canadian Army in both World Wars was a predominantly English-speaking army, in both Command ranks and it's various unit formations.
I hope this proved useful, and hopefully someone can elaborate on any of the points I was unsure on, or correct any mistakes or misconceptions I had.