Your examples are not what I mean by a French daybed. I mean one like an ordinary bed with bedhead and tailboard both tall and fixed. Second hand ones are cheap when they come up. Under £500.
I agree with Gog64 about strength. I don't think your plywood design will last long with a strong and restless adult male. I don't want to go into details but I have some experience of this. We ended up making a sleigh bed with sloping tall sides and a similar back. The front had a removable metal frame that was held on with the kind of drop release bolts used on lorry trailers.
Anyway, you seem set on your course and ridicule other ideas so I will drop out now and wish you well with it and your son.
"ridicule"? what?