as I know, we use the semi-colon (‘;’) to express multiple choices.
For example, when you start a letter (a mail) you could put:

Madame ; monsieur, bonsoir,

Since we have a couple of independent proposals from each other here (“Madame” and “monsieur”), we use a semi-colon to separate them.
It has some kind of “pick your favourite option” function.

Here’s the French Wikipedia definition:

Le point-virgule est un signe de ponctuation représenté par une virgule surmontée d’un point, principalement utilisé pour séparer des propositions indépendantes dans une phrase.

I’ve translated it in English (sorry if it’s not perfect) :

The semi-colon is a punctuation sign represented by a comma surmounted by a point, mainly used to separate independents proposals in a sentence.

[Source – Wikipédia FR]