How much does it cost to race in the Tour de France?
It's hard to come up with an exact number, but you could likely get a team in for $10 million dollars or slightly less.  The figures I have seen for "average" budgets are usually around $20 million.  Most estimates place over 50% of the budget in salaries, with larger name riders making more.  A Tour de France team is 9 riders, however, pro teams generally consist of more riders and the best 9 (currently available) are chosen for the race if the team is invited.  However, a UCI pro tour team needs to have a minimum of 25 riders and a max of 30.

Officially there is no "cost" ,per se, for racing in the Tour de France.  Teams are invited.  However, the costs are associated with getting a UCI licensed pro cycling team, which must have a full time staff and meet minimum requirements.  Theoretically a person with near magic insight could assemble a team of unknown riders and staff for around the $10 million minimum.  However, it's likely that if the team did well enough to actually be competitive, riders and staff would be snapped up by teams with larger budgets the next year, likely gutting the team.  

For a minimum 25 rider team, you are probably looking at ~$2.5 million for minimum rider salaries and salaries for a staff plus UCI fees (severely lowballed).  That's roughly $100K per rider and wouldn't cover travel costs, facilities or anything else.  ~$10 million sounds closer to covering all those things.  Or roughly $400k per rider for your 25 rider squad, only 9 of which you will send to the Tour de France.  As asked, the question is difficult to answer, because although you may need roughly ~$400k per rider for your Tour team, you have to have an additional 16 riders on staff to be considered for invitation (all at the same minimum cost).