Scroll to the bottom for the TL;DR.
Not sure why I went so deep on this, but I hope someone has fun reading it.
To figure out pronunciation, we first need to disambiguate what word this "Chasse" instance is based on. There seem to be three different words spelled as "Chasse", that each have different meanings (though with a fair amount of shared etymology).
The seems to be the most common version of a word spelled "chasse". This is the formal spelling for a specific Ballet step. In English, it can also be spelled as "sashay" ,although that spelling also seems to carry a slightly more expansive meaning than the French spelling which seems to be specifically for the dance step.
- Pronounced "shaw-say" based on Wiktionary, and my personal experience.
- This is not a good candidate for the basis of the corebook word as it doesn't really make sense in context.
This seems to be the least common usage of the word. It's one of the two options presented upon just googling "chasse". It seems to be a semi-archaic word for certain types of reliquary boxes. It is often not spelled with the circumflex over the "a", but I included it here to distinguish it from the other candidates.
- I believe it is pronounced "shass" (rhymes with "mass") based on this handout I stumbled upon.
- This also does not seem like a good candidate for the basis of the corebook word as it similarly doesn't really make sense in context.
This definition was presented the least readily by google, but seems like the best bet. This is a French word which seems to roughly translate to "The Hunt" (based on the word's usage here and in a few other articles I peeked at).
- Pronounced "shass" (like "mass" in English or "más" in Spanish, but with "sh") based on Wiktionary.
- This looks like the correct candidate as it best matches the hunting related context of the rulebook quote.
I think "shass" (like "mass" in English or "más" in Spanish, but with "sh") is probably the "most correct" pronunciation. The corebook seems to be borrowing the French word "la Chasse", an French idiomatic word for "hunting season".