Hi
If the UK website is already well-established on www.website.com then do not risk moving this to a .com/uk sub-folder. There will be no additional benefit from moving it onto the sub-folder, yet you could risk losing some organic search visibility through the redirection process.
There would be no issue for Google understanding your site structure if you go along with your plan:
www.example.com (UK)
www.example.com/fr (France)
www.example.com/de (Germany)
and so on...
We recently hosted a webinar detailing many of the considerations you should take into account when launching internationally - https://www.searchlaboratory.com/2016/10/technical-seo-for-international-markets-webinar-video/. I hope you find that information useful.
Good luck with the launch!