https://www.seat61.com/lunea.htm(There’s even a video.)
It does seem a little “adventurous” from Edinburgh although that bit of France is a right pain to get to, so the night train is an ok option.
But have you not bought any tickets yet? Between East Coast + Eurostar + night train I expect it will cost a small fortune as compared to Edinburgh-Geneva on easyjet.
The night train is the cheap bit. Paris - Mont-Dauphin direct is €177 for 4 each way on the sleeper, double that with lots of changes during the day. Eurostar is £650-ish. Ed-London is usually about £200 return. Not cheap. It is a lot more exciting than planes tho, more environmentally friendly allegedly, and makes a stop off in Paris easier. What’s stopping me booking it is the admin faff of working it all out.
If only you knew a professional admin boffin
We did a French night train when I was little, still have fond memories though I don't think we slept much!
We never sleep much on the sleeper to London, mainly as Ray insists on taking the kids to the buffet for hot choc. Bed at midnight, get kicked off at 7:30am. The French trains seem a bit more civilised.
The Edinburgh - London sleeper has just relaunched and is much more upmarket, doubling the prices which is a shame. Can't see us doing it again in the near future.