There's all kind of adventures to be had out there depending on how long you've got and how much money you want to spend doing it and you don't need an 'Adventure bike' to do most of them- before they were invented people just went on whatever they rode.
Like many here, I too have done quite a lot of miles around Northern Europe on my Monster but this year instead took my Thundercat round Brittany but on either bike the French country roads are just luurrvely.
Go old skool, get a map and pen out a route ay home before you go, don't stick too rigidly to it when you're there but avoid the tolls and motorways (unless you really want to cover big distances) and just enjoy the scenery and little towns and villages as you pass through them.