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The effect of the words "free" and "me" in the poem is to create rhythm, to make the poem more harmonious and musical.
It is only possible to discover the effect of this on the theme of the poem, if the poem is read. However, as the author decided to relate these words, we can consider that the poem has as its theme the freedom of the speaker and the rhyme between these two words was made to intensify this need for freedom.