I just came back from Italy, went to see the Formula 1 Italian GP at Monza. I would definitely hit up the Belgian GP (Spa Francorchamps) and Italian GP (Monza) as these are back to back weekends. They do come up after the long summer F1 break so plan your travel accordingly.
Looking at the various schedules for this year, it seems that the 24 Hours Le Mans race happened right around when F1 headed to Canada for a week.
Don't know if it will be the same for next year, but F1s European GP season starts from mid May with Spain and Monaco, (a pause in between to the Canadian GP and in 2013 the GP of America in New Jersey back to back with it) and then they head back to Europe in late June, ending with Belgium and Italy in the first 2 weeks of September. The 2013 24 hr Le Mans is scheduled for the weekend of June 22-23.