If you're talking about Ezra Pound's poem "Portrait d'une femme," the answer is pretty simple, in a way, I believe: Pound was a full-blown modernist writer, and modernists like Pound and T.S. Eliot are famous for their use of foreign languages of all sorts.
Both writers were American by birth but chose to live across the Atlantic, mostly in England, France, and Italy. I don't think that they used so many foreign language terms simply to show how smart they were; instead, they wrote like they lived, frequently crossing boundaries and showing a general reluctance to buy into the old ideals of nation. The devastation of the First World War is often credited with prompting these writers and other so-called "expatriates" to explore new ways of belonging.
The link below will take you to a series of critical statements on the poem that may further inspire you as you write your essay. You'll see, for example, that many critics analyze Pound's poem alongside T.S. Eliot's poem "Portrait of a lady," written or published one year before Pound's poem. The comparison seems justified; the two writers were very close, and the title of Pound's poem is simply the French translation of Eliot's poem's title.