I've been watching it for years and still can't find an answer to this question. It's no secret that they should protect themselves from blood-borne diseases. They should know that so why not wear gloves? I would never touch a bloody patient without gloves.
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Answer`s (3):
1. SoccerRefToo
Mark

These riders are tested weekly for drugs et al. In reality, unless you have open wounds, the chances of HIV transmission is minimal. The real issue is Hepatitis. Additionally, I would imagine that not every country has adopted the stricter protocols that we have in the USA.

Soccerref
2. NAP BQ
Well, you are right, they should wear gloves. Perhaps the laws in France don't require gloves. Fortunately, the riders all have blood tests beforehand to check for diseases. But the docs could spread disease to the riders!
3. John M
Most of the injuries are just road rash where they wipe it down with a sterile pad and wrap or tape it up. They would have to wear gloves all the take or waste time putting them on.
Doctors in Bear, DE