Yes, you may combine your business trips with private vacation. However, in order to get fully reimbursed for the business trip, your vacation may not be longer than 5 working days. If you stay longer, only the transportation costs from your vacation location to the business location will be reimbursed.
Example: You fly to Paris, take the train to Marseille, where your conference is. You take the train back to Paris and stay there for a vacation of 6 days, then fly back. The flights will not be reimbursed, only the train rides to/from the business location in Marseille.
Days that are needed for travelling to/from the place of business do not count towards your vacation days. More information can be found here (German only).
Attention: If you are in any way unsure whether your vacation is longer than 5 days, please contact the travel department directly and ask them for written approval of your travel plans.