For example, in the play "Much Ado About Nothing," the character Benedick says, "She's but a woman, and I am a man; and I am a fool, and she is a fool; and we are two fools together. Get you a fool of your own, and I'll get a wife of mine." In this passage, the word "fulsome" is used to mean "gross" or "disgusting."
Another example of Shakespeare using the word "fulsome" in this sense can be found in the play "King Henry IV, Part 1." In this play, the character Falstaff says, "O, thou hast damnable iteration, and art indeed able to corrupt a saint. Thou hast done much harm upon me, Hal; God forgive thee for it! Before I knew thee, Hal, I was pure, I was chaste; I was almost a saint. But thou, Hal, hast corrupted me; thou hast broken my wind in good faith, and made me a most fulsome companion." In this passage, the word "fulsome" is used to mean "corrupt" or "debased."
So, when Shakespeare uses the word "fulsome," he is not referring to something that is overly flattering or complimentary. He is referring to something that is rank, foul-smelling, or disgusting.