In the poem "Dover Beach" by Matthew Arnold, how does the image of the light on the French coast in Lines 3-4 take on a more symbolic significance...

On the French coast the light

Gleams and is gone...

Arguably, this light symbolizes hope and connection with the rest of the world. It appears for a moment, inspiring hope, then dissolves in the distance.

"Dover Beach" is a poem that taps into an existential anxiety that will become more pronounced after World War I. Arnold's narrator anticipates the existential crisis of the Modernist age. The third stanza, beginning with "the Sea of Faith" is important as well. Religion, which provided meaning in an otherwise incoherent world, is fading in power and strength, "retreating, to the breath / Of the night-wind."

The coastal setting is significant. In literature, coast lines are the borders between the known world and the Unknown. It is the the line between the firm, stable land on shore vs. the mobile and violent sea.

In the final stanza, in response to this hopelessness and uncertainty, the narrator turns to his/her love. Companionship is one's only solace:

Ah, love, let us be true

To one another!

The first line of the stanza begins with a sigh, which can indicate relief, spiritual exhaustion, or both.

For the world, which seems

To lie before us like a land of dreams,

So various, so beautiful, so new,

Hath really neither joy, nor love, nor light,

Nor certitude, nor peace, nor help for pain...

"The world," symbolized by the French coast, is not the place of abundance they had imagined. This previous sense of abundance is indicated by the use of the emphatic adverb "so." They are disenchanted by the loss of light on the other coast, causing them now to see the world as a place of absence, loneliness, and uncertainty. The only thing on which they can depend is the presence of each other, "on a darkling plain." 

"Darkling" is both literal and metaphorical here. It is night, so the sky is becoming dark. However, the world is also becoming a darker and more frightening place:

Swept with confused alarms of struggle and flight,

Where ignorant armies clash by night.

There is parallelism between darkness and confusion, as well as ignorance. There could very well be an ongoing battle on that other coast.