If this is confusing you, "Gently, gently!" has the same meaning and is an easier translation.
Doucement? Easy here means 'Not difficult' or 'Take it easy, it takes time'??
It means "take it easy" as in what one would say to a horse to slow it down or calm it down. Or what you would say to a person who hit you too hard when all you needed was a gentle tap. Or what you tell someone who slams on the brakes too hard.
Literally, "doucement" comes from the adjective "doux/douce" meaning soft or gentle.
Would "softly, softly" work here George? I have heard that said a lot when urging someone to calm down and tread carefully.