When Québécois people in my presence said 'I am/we are French' it wasn't in just a linguistic context. It was the same phenomenon as all the US Americans calling themselves 'Irish' or 'Scottish'. They did say it in English though, even when I was speaking to them in French.
Come to think of it, that reminds me of the story of an Irishman and his mother who were visiting the USA. They were speaking Irish on the street in San Francisco and a local told them 'This is America, you need to speak English here.' They explained that Irish was their first language and he started telling him he was Irish too.