I must admit that I've confused these two words - complacence and complaisance - many many times over the years.
I always had to look them up to make sure I had the right one, which is why I came up with this little method of keeping them straight in my head.
Complacent refers to someone who is pretty satisfied with himself and his life. It's often used to describe complacent rich kids or the complacent 1%. I just remember that compl-ACE-nt has the word ace in it, because it means you think that you're pretty ace!
If the word looks French to you, then this tip will be easy! Complaisant refers to someone who is eager to please - or in French plaisir - other people. Even though it's pronounced just like complacence - the two words are homophones - when I'm on my own, I tend to say complaisance with an exaggerated French accent to help me remember which word I'm referring to.