Here's a timeline link to the history of coffee which is fairly interesting. One of the things it mentions is that Americans took up coffee drinking after the Boston Tea Party. There's also a mention that some sources have claimed coffee arrived in Canada before it arrived in the US.
The History of Coffee
Looking at the timeline, it seems to me as though there was enough of a possible UK and French coffee influence in terms of coffee arriving in Canada, that it would be impossible to say that Canadians drink coffee due to the influence of one or the other. Especially since coffee wasn't unknown among immigrants from nations other than those two and I'm not sure that there would have been much of an impact in the west based on Quebec, say, or even the UK.
Coming from Eastern Europe, Mennonites arrived with a samovar but they also had coffee, and used roasted barley as an ersatz coffee in hard times. I wanted to buy the family samovar when it came up for auction a few years ago but was outbid by a cousin. So tea drinking wouldn't have been due to a British influenced Canada either.
Our mum served us tea when we were sick. Tea and Heinz tomato soup.
It was really the only time we had either.