I don't understand the exact meaning of the following word highlighted in red.
We're assuming your significant other is not French and you do not have the green light to fool around.
I'd be most grateful if anyone'd help me.
The implication is that the French are more "relaxed" about monogamy. In America, a politician who cheats on his wife will have a difficult time retaining the favor of the public.
In France (and some other European countries) it is expected that powerful men will have mistresses.
Keep in mind this is stereotype.