Rousseau began writing in 1750 (Discours) and Goethe wrote the first portions of the Urfaust (original fragment of Faust) in 1772, therefore it is reasonable that there may be influences of Rousseau's philosophical ideas in Faust Part I. It is harder to maintain that Rousseau's ideas appear in Part II, which is developed in a Classical vein and holds extensive Classical allusion. In 1777, Goethe repudiated Romanticism, which sprang from his Rousseau-influenced ideas in The Sorrows of Young Werther, which actually gave birth to Romanticism. His repudiation came when, in 1777, he saw that a young woman who had drowned herself went to her death with a copy of The Sorrows of Young Werther in her pocket.
You might say that Faust becomes Rousseau's man of feeling beginning from "Witches' Kitchen." It is here that he sees the image of Helen of Troy in a magic mirror and, as a result, agrees to Mephistopheles’ (Mephisto’s) coercion to take the witch's love and youth potion. As a result of the potion, his passions are awakened, after having slept for his lifetime, and he directs his feelings at Gretchen.
Throughout their courtship and his ultimate seduction of her, his passions and feelings take more sway up to the moment that Faust, under the control of Mephisto, meets and slays Valentine, Gretchen's beloved brother. The ultimate demonstration of his feelings occurs in "Dreary Day: A Field." Mephisto has told Faust of Gretchen's suffering--though it is not shown on stage--and Faust loudly berates him and curses him for withholding the information from him:
Treacherous, contemptible spirit, and thou hast concealed it from me! ... Stand and defy me with thine intolerable presence! ... [Thou] hast concealed from me her increasing wretchedness, and suffered her to go helplessly to ruin! ... Dog! Abominable monster! ... O woe! woe which no human soul can grasp ...!
This and the scenes that follow are considered by most critics to be Goethe's crowning achievements for the heightened realism of intense emotion they carry. Faust demands that Mephisto rescue Gretchen: "Rescue her, or woe to thee! The fearfullest curse be upon thee for thousands of ages!" Mephisto points out the limits of his power, but Faust, in his love and horror, is adamant: "Take me thither! She shall be free!" Mephisto cautions him about the "guilt of blood" that "still lies upon the town" because Valentine was slain. Faust scorns the mention of his own guilt and demands, "Take me thither, I say, and liberate her!" Mephisto capitulates, within the limits of his power, and says, "the magic steeds are ready, I will carry you off," to which Faust echoes, "Up and away!"
In "Dungeon," the emotion crescendos and grows even more painfully realistic and intense as Gretchen, half crazed, insists upon her punishment, and Faust, despite his desperation and despair, is unable to convince her to allow herself to be rescued. These scenes certainly show Faust as a Rousseauean man of feeling, which is defined, in short, as one who declines to interrupt the flow of passion and feeling and further declines to act within reasonableness and select, combine, and choose the right words and phrases that create the witty and persuasive expressions of language used and preferred by a rational--not a feeling--man [person].