If you are correct and the old site is already distrusted by Google, then I would keep the old site as separate from the new site as possible. This means that you should avoid any kind of linking between them... as tempting as that might be. If the site has been flagged for selling links, it's likely that links from the old site won't be that helpful in any case... and the new site could well be seen as a link buyer.
I would also avoid common hosting between the two. I myself take a very conservative approach to anything that might identify a connection between the sites. At the moment, you are correct that the same content in different languages won't be seen as duplicate. Too many link sources in common, though, linking to both sites, might be problematic. Google in fact once used the term
"Similar sites" to describe sites with common link sources. This suggests that if a niche is small enough or specialized enough, Google may have statistical methods to identify similarity, even across different languages.
Though this may sound bleak, from what Google has said publicly, I believe that they do prefer to "rehabilitate" domains and sites rather than to ban them. I don't know what the waiting period is... but clearly you would be expected to reverse some actions and demonstrate that you're not going back to the dark side, etc. I don't know whether this is the kind of thing that John Mueller might give you a direct answer on, but I'd give it a try.
If your old site really is content rich, I'd work on updating and/or improving it. Go for content that is absolutely extraordinarily good. I would also, as lammert suggests, phase in the rel="sponsored" tags. How you work that out with your link buyers is likely to be awkward, at best... but chances are, in the long run, that tagging the links while keeping them up is the best perhaps the best approach for you and the buyers, as they too have probably also been identified.
Whatever you do, avoid appearances of manipulation as you are cleaning things up. You don't want to appear that are reacting to changes in ranking by calibrating your actions accordingly. See this discussion for background on why I say that...
Google's Rank Modifying Patent for Spam Detection Aug 18, 2012 https://www.webmasterworld.com/google/4486158.htm [webmasterworld.com]
I'm relatively certain that I've seen the rank modifying patent in action, and I believe that it is something that Google has both patented and implemented.
