On the touring version of the Raid Pyrenean the distance is 790km. If you manage this in the 10 days (240 hours) allowed you have to maintain an average of 3.29166666'. Allow 12 hours a day in the saddle then you have to do 6.5833333' km/h.
The unladen randonneur version is 720 km for which you have 100 hours, 7.2 km/h overall, or if you ride for only 50 of those hours, a modest 14.4 km/h - only slightly harder considering the reduced weight - will get you there.
So for mountainous stuff, assuming I haven't cocked up the arithmetic:
Laden: c. 7 km/h (4.375 mph) ;
Unladen: c. 14.5 km/h (9.06 mph)