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Translated pages never are considered duplicates by Google. I suppose that you're going to experiment with multilingual, not multi-country targeting. In this case you can create the "foreign languages" versions of your site under their respective subfolders (/fr/ for France, for instance). There, you will replicate the English site, with the exception that you will have also translated pages. Be aware: the "home page", the menu and all the template should be localized too. In the case of the not-translated pages, you can decide to canonicalize them to the original version, but implementing the rel="alternate" hreflang="x" so to suggest Google that it's that URL that you want to show to users using a given language in their search and browser. 100% duplicated content - and a situation like this one - is the only moment using a not  self-referential rel="canonical" URL and the hreflang at the same time is justified (and doesn't cause problems).

If you do as Fransisco says, and move the entire site correctly...you should just go to Google Webmaster tools and move the URLs there. If you have GWT approved for both domains, you just follow the guide in there to move the site from a Google perspective.

Thanks a lot! I will definitely try that.