Final answer:
Walt Whitman, known for his pioneering use of free verse in 'Leaves of Grass', was the American poet who significantly influenced French symbolists like Stéphane Mallarmé and Paul Verlaine.
Step-by-step explanation:
The American poet who strongly influenced the French poets Stéphane Mallarmé and Paul Verlaine was Walt Whitman. Whitman's use of free verse was a significant departure from traditional poetic forms and allowed for a greater range of expression. This innovation was particularly impactful on the French symbolist poets, including Mallarmé and Verlaine, whose work similarly explored the boundaries of poetic form and content. Whitman's celebrated collection, Leaves of Grass, with its embracement of everyday language and subjects, contributed to this profound influence on French poetry.