Not everyday is a good day. Adrien knows that. He also knows that his purring is useful to calm people (especially children during an akuma attack. Kids like the sound of it and that way he can do his job quickly).
So when Marinette has a bad day
he tries to do the same she does when he feels down: be there for her. And he use his purr to calm her a little. This purr is lower and longer than the ones he uses for kids, since he is not in a hurry and wants to express better what he feels.
Also forehead touches are a Marichat thingy, fite me.
Take a look at all of the amazing things that you have done up to this point. Yes, there may be bad decisions and mistakes scattered here and there, however these do not erase all of the good that you have done. Allow your positive actions to shine through, radiate your soul, and continuously remind yourself that you are always capable of truly amazing things.