Of course, France is a country that makes secularism by far a huge part of its national identity; so part of "being French" certainly involves leaving religion at home (which includes not wearing christian necklaces, or head veils, or turbans, etc).
That description of laïcité is very much a rose-spectacled one. In practice it has always meant an in-group seeking to suppress the culture of another group it looks down upon and wishes to exclude from power. It used to be about the elite marginalising peasants from the Vendée, now it means the elite marginalising Muslims in the banlieue. It's not a national identity, it's a state identity and I don't see that that kind of hypocrisy deserves to be treated with respect.