In Germany I must have an ID with me at all time (passport, national identity card, ...) by law yet nobody but the Polizei can request to see it.
The law you quote says that to have a service dog, you must be a recognised disabled person. Not that you must have or present a disability ID. The wording is very clear, as is the wording of the european regulation I presented earlier in this thread.

When Air France are demanding to see proof of your disability in order for you to benefit from preboarding for example, they are breaking the law. They should not. A grocery store even more, you should consider refusing next time and if they refuse to serve you, call the police here and there.