Like Carrie and Hurstwood, Drouet is a type. Specifically, Drouet is a drummer (a.k.a. travelling salesman) and (thanks to our narrator) we all know what that means:
Lest this order of individual should permanently pass, let me put down some of the most striking characteristics of his most successful manner and method. Good clothes, of course, were the first essential, the things without which he was nothing. A strong physical nature, actuated by a keen desire for the feminine, was the next. (1.16)
So Drouet is basically a clotheshorse who is forever on the prowl. And true to form, the moment we meet the guy, he's shamelessly hitting on Carrie, right?
Drouet seems to have some game—he bags Carrie, after all—but ultimately he's kind of emotionally clueless: "There was something delicate and lonely in [Carrie's] voice, but he could not hear it. He had not the poetry in him that would seek a woman out under such circumstances and console her for the tragedy of life" (11.20).
Maybe the effort Drouet puts into picking out his ties would be better invested in, say, listening? Such displays of insensitivity seem to contribute to the demise of his relationship with Carrie. Drouet's character is especially important in this regard since one of the novel's chief concerns is exploring the breakdown of relationships between men and women.
We learn that Drouet's also kind of a wannabe. The narrator remarks,
He loved fine clothes, good eating, and particularly the company and acquaintanceship of successful men. When dining, it was a source of keen satisfaction to him to know that Joseph Jefferson was wont to come to this same place, or that Henry E. Dixie, a well-known performer of the day, was then only a few tables off. (5.2)
What, does Drouet think successfulness is contagious or something? In this way though, his attitudes shed light on one of the book's central themes concerning the question of how success in America is really attained.
But don't get us wrong—Drouet's not such a terrible guy; we get endorsements of him (at least initially) by Carrie, Hurstwood, and the narrator. We're told:
Hurstwood liked Drouet. The latter's genial nature and dressy appearance pleased him… Drouet had what was a help in his business, a moderate sense of humour, and could tell a good story when the occasion required. (5.11)
To Carrie "and indeed to all the world, he was a nice, good-hearted man. There was nothing evil in the fellow" (7.3). The narrator underscores his generosity: "Yet no beggar could have caught his eye and said, 'My God, mister' I'm starving,' but he would gladly have handed out what was considered the proper portion to give beggars and thought no more about it" (7.3). And, unlike Carrie, Drouet puts his money where his mouth is and helps out the homeless man whom she and Hurstwood don't even notice.
So maybe there's more to this "drummer type" than meets the eye?