Are rare burgers safe?
Applying USDA standards (which may or may not be the 'same' as elsewhere, but (IMHO) serve as a reasonable standard for "Safe") Hamburger must be cooked to an internal temperature of 160°F [71°C] in order to be 'Guaranteed Safe', which is typically defined as 'well done'. 

On the other hand hamburger may be perfectly safe at medium rare to rare (120°F - 49°C) depending on how the beef was raised and processed. Actual cases of serious food borne illness from even raw meat are fairly rare (or should I say uncommon? ;) ). As far as I can tell the French are doing nothing 'special' to neither decrease nor increase the risks involved.

Many restaurants (in the US) will specify on their menu some thing like:


  All burgers cooked med-well unless otherwise requested




A variety of circumstances from acid levels in the meat to the application of dyes may cause meat to appear 'pink' but be perfectly safe, ground beef may also appear to be brown, but may not be safe at all. Pink is not necessarily a good standard. 

Since you are unlikely to get an 'accurate reading' carrying your own food thermometer with you where ever you may go (if your food sits on the counter for a while before getting served the temp by the time it gets to you will be less), the best test to apply in a restaurant is 'cooked' vs. 'raw'

A quick Google search "Hamburger Rare vs. Raw" will display a myriad of images from which you may discern what you are comfortable with. 


  By 'serious' food borne illness I am referring to things which might
  require a doctors care or put your life in jeopardy. While lower-grade
  illness maybe 'unpleasant' they are not necessarily 'unsafe'
  
  
  
  "As far as I can tell" denotes the inability to prove a negative.
  Having looked through the Anses website, particularly their
  section on 'nutrivigilence' and 'animal nutrition and welfare' looking
  for any exceptional methods (radiation treatment, quarantines,
  chemical therapies etc) that might have the goal (even if not the
  effect) of making the beef supply more safe...I found nothing to cause
  me to believe that they are actually doing anything exceptional (over
  and above US or EU standards)