I’m afraid this question is far too localized to match SE goals but well, at least it’s not homework…

One first comment. You wrote:

only to find that the Fois means literal time (as in time of day).

This is incorrect. Fois does mean “times” here like in “three times two friends”. It is not restricted to literal time.

About your wine, my best guess for an idiomatic suggestion is:

La cuvée des six amis.

Beware not to capitalize every word like it is done in English (although that rule is not well observed in the next samples…)

Some similar wine names:

Why don’t you just name it in Italian instead? It is a French blend? Or some special connection to French wines? “Sei amici” solves your problem and still lets you use a romance language from a country that produces a lot of wine.