Mmmm... I see on their website the Genki school in Tokyo does not offer a long term course, so I don't think I'll try to go there, but I'm still interested to read more about it.
You can still study there long-term, the Tokyo school just can't get you a student visa. If you are a French citizen you can study there up to a year on a working holiday visa, so that shouldn't be a problem.
I think GenkiJACS Fukuoka/Tokyo are not very different except that at the Tokyo school there are more short-term students, and more students in general. I studied there for 5 weeks in the summer and 2 weeks in the winter.
Advantages
-Courses are aimed towards speakers of European languages, as opposed to other schools where there may be a lot of Chinese and Korean speakers. At lower levels this makes a big difference.
-The reception staff are very helpful and speak English well. If you have a problem during your stay (e.g. I dropped my wallet at one point…) they can help you out.
-The school will arrange accommodation for you if you want. Probably quite a bit pricier than finding a place by yourself. In the summer I stayed in a sharehouse with both Japanese people and various foreigners, that was what made my stay so fun and memorable. I'd recommend that option. In the winter I was in a one-room apartment. I already had friends so it suited me well, but it could be isolating.
-Teachers are very friendly and have a sense of humour. Generally they speak English well, especially the ones assigned to beginner classes.
-Class size was between 2 and 8 people, usually about 4, so you get opportunities to speak and ask questions.
-Friendly and social atmosphere. They arrange a dinner or similar every week for the students (about 2000 yen), occasionally they organise other events or trips.
Disadvantages
-I found that they concentrated on a few grammar points per week but didn't come back and review them except when they happened to come up later. In this sense you have to take some responsibility for using what you've learnt so you don't forget. This approach didn't suit me because I have a very good short-term memory and didn't need to practise one or two verb forms repeatedly for a whole week; I'd rather go quickly and have more reviews.
-They tend to stick quite rigidly to the material in the textbook.
-At lower levels they spent too little time on kanji (well, they were just following the Genki books and they are very slow at teaching kanji…)
-In the summer I had trouble with some other students in my class who were rather disruptive (fortunately they left after a couple of weeks). Most students there are short-term and might not be as serious as you about learning.
Whether it's "intensive" or not depends what you're used to I guess. These are the only formal Japanese lessons I've ever had so it's hard for me to say. At beginner level they cover about 1 chapter of Genki per week, but it is possible to repeat levels if you can't keep up the pace.