I would say that the tone of the first six lines is calming and peaceful. I feel that the writer's tone evokes the same mood in the poem's readers, so they are closely related in this poem. The first six lines describe the narrator overlooking the white cliffs of Dover at sunset. He can see the French coast across the channel.
I feel that the tone is most set by the adjectives that the poet uses. "Calm," "full," "fair," "tranquil," and "sweet" all seem to put the narrator at peace, and consequently the reader as well. It sounds beautiful. I mean there is a reason that I proposed to my wife on the beach at sunset. It's a cheesy cliche now that I look back at it, but she did say yes :)
I also think that the familiar iambic rhythm is calming and peaceful as well. It's familiar to poets and readers alike. Add to that the fact that the opening 6 lines rhyme at times. That regular rhythm and rhyme creates a feeling of calmness and being clearheaded. Shakespeare often has his characters break rhythm and meter when they are feeling confused, and they hold perfect rhythm and meter when calm and at peace. For example, Romeo and Juliet speak to each other in perfect sonnet form when they first meet. Matthew Arnold uses that technique in the first six lines.
One last thing about the tone. It sounds almost conversational. That's because of the use of enjambment. Enjambment is when a line of poetry spills over onto the next line.
The sea is calm tonight.
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,
The above is the first 4 lines. Line 2 spills into line three with no punctuation. Line 3 spills into 4 the same way. This allows the poem to flow from line to line instead of being read line by line. It's more natural to how people talk, and converse with each other; therefore, it sets a more casual tone. Line 2 also makes use of the poetic device called caesura. That's fancy talk for a poet putting a pause in the middle of a line. Arnold does it with a comma. Here again it adds to the calm tone. It slows down the line, because it forces a pause. It's like the speaker says something, thinks about it, and then adds to it. There is no rush.