Why does the Dassault Falcon 7X's cockpit have ashtrays?
In the United States, the smoking ban only applies universally to air carriers on scheduled flights. The regulation states


  §252.4   Smoking ban: air carriers. Air carriers shall prohibit smoking on the following flights:
  
  (a) Scheduled passenger flights.
  
  (b) Nonscheduled passenger flights, except for the following flights
  where a flight attendant is not a required crewmember on the aircraft
  as determined by the Administrator of the Federal Aviation
  Administration:
  
  
    (1) Single entity charters.
    
    (2) On-demand services of air taxi operators.
  
  
  (c) Nothing in this section shall be deemed to require air carriers to
  permit smoking aboard aircraft.


So for essentially all of the Falcon's missions, such as Part 91 corporate flights, and private charters under 10 passengers, smoking is permitted, as long as an "adequate number of self-contained, removable ashtrays" are provided (14 CFR 23.853(c)(1) or 25.853(f)).

Said ashtrays from a factory photo:


Closeup found here: