In French it doesn’t mean anything. It’s just a name. It would be like the “-ard” in Richard, Bernard, it used to mean “hard”, but nowadays, it’s just part of the name…

Note that it’s just pronounced “o”. Yes, that’s right, it’s five letters, and it’s pronounced just like one. You don’t pronounce the ‘l’, the ‘t’, or the ‘e’, and ‘au’ makes the ‘o’ sound. That’s just a quirk of French.

I’ve read some forums online (it appears to be just speculation from anonymous users so I’m not sure there’s a point giving links). Also my knowledge of ancient Germanic is zero, so take this with a grain of salt.

• One possible explanation is that it comes from old Germanic “ald” meaning “elder”. So in English it would be like in the names “Archibald”, “Donald”, “Gerald”, maybe.
• Another possible explanation is that it comes from “wald” which means “to rule, to govern”. In English this would be like in the names “Oswald” or “Torvald”, for example.

Some also mentioned that the different between “-ault” and “-aud” might come from different regions and religions of France (catholic vs protestants, south vs north, east vs west…), but nothing really clear.

The archaic French suffix -eault and phonetically similar ones -aut, -eau, -au, -aud, -ot are typical diminutives, e.g.:

Pierre  →  Pierrot  
Jean    →  Jeannot  
Chien   →  Chiot  
Petit   →  Petiot  
Arbre   →  Arbrisseau

thus

Boisson →  Boissoneault 

In that particular case, the root of the name cannot be the modern boisson (beverage) as it wouldn’t make sense for a family name and also because boisson was likely less used than beverage / breuvage.

The root is almost certainly what we now call buisson, meaning “bush”.

Buisson was indeed spelled boisson in old French and was already a diminutive of buis or bois.

So Boisso(n)neault and variants like Boissonneau are naming a family originally living near a small bush, a grove, a stand of wild shrubs, a.k.a. a buissonnet, .