I think that it is possible to go directly to the BOE's to offer your services, but I believe that their hiring process are probably already well underway for the coming school year. I haven't ever seen or heard of any dispatch companies down here though.
I think that most non-teaching part-time jobs would be in violation of your visa, but if you're not worried about that, there are some jobs at bars and the like.
I know of some foreigners who operate marine sport related businesses that cater to the military down here, but I have never heard of anyone working in the tourism or marine sport industries that didn't own their own company. That being said, if you can make the right connections while your here, who knows what's possible!
Most of the people that I know work in the English conversation industry and a few people work in IT. There are some IT positions available here if you have that kind of knowledge. There are also jobs related to the base, but I've heard that most of those go to the spouses of military personnel. Also, if you look at the military job websites, most of the low skill jobs listed are for local hire only, so those of us that are not permanent residents cannot hold those jobs. For a large list of government jobs in Okinawa, I'd check out usajobs.gov and search for Okinawa. Hmm... Now that I write that I wonder if you are an American. You speak French and English though so...
Anyway, I hope that helps.
