What is the best visa option for a 6-month stay in Thailand for a French expat?

I do not fully understand the logic of doing exemption first, but not extend, then getting a tourist visa and extension. If you want exemption you may also want to extend it for another 30 days.

You may be better off with two single entry tourist visas though. Each can be maxed to 90 days, yielding the 6 months you aimed for. You need just one trip abroad.

Or work with exemptions, then it's 3 x (30 + 30). So an extra trip abroad and an extra extension, but two less visas.

The multiple entry tourist visa is an option too but not strictly necessary as your nationality qualifies for exemption. It can be used to squeeze 9 months stay out of but if you need only 6 I see no real advantage of an METV. And it's not so cost effective.

Forget the idea of online education visa. You need to attend school not study online as you can do online from home.

Technically flying in you have more than one 30 day exempt entry and extension. You can fly in as often as you want until an imo stops you

To spend my winters in Thailand, I used to get 3 each 60 day visas, resulting in me making 2 visa runs to the Cambodia border. Bit of a pain in the ass but it worked out OK

If you're trying to go for 6 months then I wouldn't bother trying to use an education visa.

Easiest would be applying for a multiple entry tourist visa from your home country's thai embassy (most likely through the evisa website) before you travel to Thailand. This visa is valid for 6 months from the day it's issued by the embassy and while this visa is valid, you'll receive a 60 day tourist entry stamp every time you enter Thailand. You can also apply for a 30 day extension once per entry.

So apply for visa, arrive and get 60 days and apply for extension (90 days total) then go to a neighboring country to explore SE Asia a bit and when you return you'll get another 60 day stamp and can apply for another 30 day extension (90 days total). Now you've gotten your 6 months.

If you apply for a six months Multiple Entries Tourist Visa (METV) you can well planned get up to 9 months in Thailand. But if you’re a french citizen you need to apply from France, ore else you’ll just get a single entry 60+30 days.