Think some of you being a bit harsh on the OP who is clearly trying to information gather - a sensible approach. Most unlikely to be over weight (3T?) with household and personal effects. Usually bulks out first.
He is exempt from tacho regs under EU law, but yes, it would make things much easier if stopped to use the tacho and abide by drivers hours law.
However, if he carries a laminated copy of the relevant exemption in the language of each country he passes through, shouldn’t have a problem.
Reckoning on 14 mpg will be about right. Might do a bit more, that will be a bonus.
To think that the round trip is do-able in 3 days is deluded. It will be a FULL 3 days to get there, possible more if any major hold ups, also depends where starting from in the UK.
I would rent the truck for a week(better rate) and plan 3 days out, a day off driving to unload, 3 days back … and you might run into the 8th day.
I did a very similar trip to near Toulouse, South of France some years ago, but only had the one country to think about.