It is somewhat difficult to identify the form of Shelley's "Love's Philosophy."
It certainly is not a sonnet, because a sonnet has--by definition--14 lines, and Shelley's poem has 16.
Is it an ode? An ode is a poem that is written in praise of, or dedicated to someone or something that has inspired the poet. Does Shelley's poem fit this definition? The poem is addressed to someone with whom the poet would like to "meet and mingle" in romantic fashion. Yet there is no praise for this person in the poem. Rather, the poet repeats, through various examples, that it is "a law divine" that various beautiful phenomena of nature should meet and mix: "fountains mingle with the river," "the mountains kiss high Heaven," "the waves clasp one another," the "sunlight clasps the earth," etc.
Perhaps it is safest to say about the form of "Love's Philosophy" is that is a beautiful poem consisting of two 8-line stanzas. The rhyme scheme in each stanza is ABABCDCD. The poet achieves formal unity by ending each stanza with a question addressed to his beloved.
It is also interesting to note that subject of Stanza 1--fountains-- rhymes with the subject of Stanza 2--mountains.