Nice thought but we actually like riding in the mountains and have quickly got bored when we've followed river/canal routes in the past, although a few flat days here and there are very welcome. Also we're only 23 miles from Portsmouth ferry port.
Well, it's obvious then
Down through the centre of France via the Massive Central
At the Med hang a left to just beyond Nice
and then follow the curve of the Alps all the way to Zagreb!
That should be enough mountains to last a summer, and probably in all seriousness about the same horizontal distance as the flat river route.
You will of course be doing several Everest's this way, but it'll keep you fit.
I'd suggest loading up the bike with several changes of clothes, a big tent and don't scrimp on the cooking kit all to ensure to have a weight to make the ascents of the Alpine passes worthy of the challenge