You got a link to your source on that?

Merriam-webster says mousquet came from the Old Italian moschetto meaning a small artillery piece. It's also a term for a male sparrow hawk. Which there was a traditio of naming weapons after animals.

https://www.merriam-webster.com/dictionary/musket

The Wikipedia page for musketeer says this:

The Musketeers of the Guard were a junior unit, initially of roughly company strength, of the military branch of the Royal Household. They were created in 1622 when Louis XIII furnished a company of light cavalry (the "carabiniers", created by Louis' father Henry IV) with muskets.

https://en.m.wikipedia.org/wiki/Musketeer

So the term Musketeer comes from the fact that they are armed with muskets. I cant find anything about a mousquet being a place on the belt to hold stuff.