If you look closely at the directions that Arnold takes each image and thought in this poem, it shows itself to be pretty pessimistic. It starts off with such a beautiful description of the night, a calm, serene oceanside view of the moon and sea, that the mood right off is one of beauty and tranquility:
"The sea is calm to-night.
The tide is full, the moon lies fair
Upon the straits; on the French coast the light
Gleams and is gone; the cliffs of England stand;
Glimmering and vast, out in the tranquil bay.
Come to the window, sweet is the night-air!"
This description is calm and beautiful, so one might think that Arnold is writing a pretty, placid reflection of his evening. However, note closely how he takes this beautiful scene and tinges it with pessimism. Right after the above lines, he brings in a contradicting conjunction. He states, "Only," which indicates that he is admitting the beauty of the scene, but saying it would be more beautiful "if only" and then he describes the waves as a "grating roar" on the pebbles, and that the entire ocean itself brings "the eternal note of sadness in". So, what to one person might seem a gorgeous, calm and uplifting ocean scene, Arnold sees as eternally sad and melancholy--definitely a pessimistic view.
From this point on, the entire poem is pretty pessimistic. He believes that everyone who has ever seen this ocean tied it to misery. Sophocles tied it to the "turbid ebb and flow of human misery". Then, he states that he feels that faith, goodness and joy are leaving the world that he is in, that it is "retreating."
In the next stanza he attempts an optimistic thought as he pleas to his love that they need to "be true to one another," which is a nice thought, but he says that they need to because there is no "joy...love...light...certitude...peace...nor help" left in the world at all. He even puts the image of him and his love being "true" to one another on a "darkling plain"; so, as they strive to bring goodness into the world, they are surrounded by darkness that keeps getting darker. Overall, a pretty pessimistic poem, I would say.
I hope that those thoughts help a bit; good luck!