, there isn’t an English Army, there is the British Army and you don’t have be British to serve in it, take the Gurkhas for example. Neither are you restricted to serving in only one countries forces. Many people have served in the British Army and gone to Australia and served in their Forces and vice versa.
French people don’t get a visa on arrival and if someone did get one on arrival it wouldn’t last 30 days but barring that there aren’t any issues with the visa exempt entries that you have described.
, as someone who runs out of talent quite often in a motocross bike, it’s been cheaper to get fixed up in Thailand than paying to park at the hospital in the UK!