I am voting for HEC-Paris.
HEC-Paris is a great well-known B-School. Constantly ranked in the top 5. While being the second best B-School in France, its direct competitor is IESE (my personal opinion). HEC will open all of the doors for you in Europe, including UK. It is a bit similar to LBS, but with less UK specific recruiting.
Additionally, since you know French/German/Italian, are in Europe, you should no issues with HEC and expanding your network and knowledge.
Reason for me not to choose Cambridge -
You already have Oxford on your resume, which is pretty much a similar school to Cambridge. These are new up-coming B-schools, but not top notch yet. This might change in the near future. With Cambridge you are really limited to UK. Yes the name carries the weight, especially for people that don't particularly know about business schools. But outside of the UK, HEC-Paris dominates. What's the point of Cambridge name, when you already have Oxford?
My personal take - If I was you, I would go to HEC, enjoy my time there. Get to enjoy a new place, a new institution which is very different to my previous school. Expand my network to France and other EU countries. You will not have an issue getting the job you want with either business schools, pick the one that will make your time worth it. I would say ignore the cost, as the difference is minimal in the long-term.
My personal ranking for European MBA:
1. LBS/INSEAD
2. HEC/IESE
3. Oxbridge