Yes, you can ride it any time. The following will be of use to you:
Roads to Ride: The Arenberg Forest
Would be at the far end of a 100km round trip to Roubaix. You can try to find other sections of pave too, they’re all numbered / waymarked.
Here’s the detailed route of this year’s race. With this and a bit of time on Google maps, you can get an idea of where to go. Some sections, like Cysoing are quite obvious…
http://www.lesamisdeparisroubaix.com/itineraires.html
Oh, and you’ll even be able to do a cheeky lap or two of the finishing velodrome. Away from race day, somewhat disappointingly, it’s not some hallowed place of cycling pilgrimage, but a manky municipal sports complex in a scruffy bit of the already scruffy Roubaix. There is now a fancy new indoor velodrome right next to it, however.
It’s ‘fun’ to ride, but hard work. Enjoy!
