As far as I know, there is no such thing in French, though the abbreviation nbr can be used if there is a lack of space.
By the way, the numéro symbol № (or n°) is rather used as # in English, e.g. in Exercice № 2713 for Exercise #2713, than as a shortcut for number of.
Une abréviation courante est Nb
Nb étudiants: 307
Nombre or nombre de isn’t usually abbreviated in plain sentences in French. Among neat-looking¹ abbreviations, except for “n. d.” which would likely be ambiguous, “nb. d.” appears to be the only possibility (but classified as a retranchement multiple and advised against).
In telegraphic style, outside of a sentence, Nb is however often used for nombre de (cf. Richardshorm example).
Notice that numéro (which is also translated as number and abbreviated # in English) has a standard and sometimes mandatory abbreviation when followed by a number: no (the letter o is found in exponent¹), plural would be nos.
1. More details in Orthotypographie, or probably any other specialized book on the topic.