I will put 99% money on it, Lille FIS West (it’s ATC for Lille approach & also Lille East now) will give you VFR clearance above FL120 (subject to LFCBA1A status which also affect IFR routing to CMB VOR anyway), 1% worst case it’s OCAS up to FL115 
Don’t plan on over FL115, unless you have the phone number of some Paris Control manager. Edit : maybe Lille can get you a higher clearance given with how little traffic they have.
Why would he call anybody when flying IFR?
Edit: I missed few posts above “VFR” :)
I would fly at FL080 if there is any headwind, or FL150/160 if there is any tailwind. But FL080 in IMC = ICE especially at this time of the year, and this is an issue for legs filed VFR to get shortcuts. The tactic for IMC would then be to ask if a change to IFR would still enable that routing.
This trip was finally done here.
The VFR sections were done with some issues, which would be well known to any pilot who has done any significant VFR flying. In particular, while French ATC will generally sort out CAS access for you, they do not coordinate on restricted or prohibited areas and will happily leave you to bust them. And the same will happen if flying VFR from Switzerland to France across the SE border which is lined with these restricted areas and you will bust one of these immediately you cross the border; Swiss ATC won’t stop you doing it (they may warn you but they are not required to).
Whereas if you fly IFR none of this is an issue. So it pays to get an IFR clearance as soon as possible, once the VFR flying option is no longer needed.
