None of those answers (or these ones) quite hit the nail on the head, but it’s one of those questions that’s easily answered by picking up a dictionary:
From Collins English Dictionary 21st Century Edition. In France, they usually write it “N°”.
When I read this my first thought was “it can’t be so” but I couldn’t pinpoint what was wrong (my French is rather rusty). After some thought (and a visit to Babelfish) the difference between nombre and numéro occured to me:
My [phone] number is … = Mon nombre est …
It’s on page number three = Il se trouve dans la page numéro trois
Actually, I think the French use numéro for phone numbers (e.g. Vous vous avez trompé de numéro = You’ve got the wrong number).
I think the distinction is that you use nombre to mean a general number (Dans un petit nombre de cas = In a small number of cases; Garçons et filles en nombre égal = Boys and girls in equal numbers)and numéro to denote a specific number in a series, e.g. phone numbers, house numbers, car registration numbers etc.
But, IANA native French speaker, so don’t quote me on that…