If you sat Mr. French down at a job interview and asked him what his biggest strength is, he would probably tell you what he tells his mob boss, Frank Costello. He would say:
FRENCH: I'm reliable.
And even though he's a total psycho who has killed dozens of people, you have to give him this.
Mr. French is a pretty great second-command for any mob boss because he always does what he's told, and he always does a pretty clean job of it. He's also someone who can straighten out the people who don't realize that Frank Costello runs the neighborhood.
When he first meets Billy Costigan, for example, he pulls Billy away from a guy he's beating on and introduces himself by saying:
FRENCH: I'm the guy that tells you there are guys you can hit and there's guys you can't. Now, that's not quite a guy you can't hit. But it's almost a guy you can't hit.
Mr. French understands the subtleties of his underworld hierarchy and wants to make sure Billy understands them before he gets himself killed.
The thing about Mr. French that comes out most strongly (apart from his skill for murder) is his loyalty to both his boss and his neighborhood. In most cases, he'd take a guy like Billy and mess him up. But instead, he says:
FRENCH: I f***ing know you. I know your family. You make one more drug deal with that idiot f***ing cop-magnet of a cousin of yours, and I'll forget your grandmother was so nice to me.
Think of it: French is so loyal that he's willing to cut Billy some slack just because Billy's grandmother was nice to him decades ago.