I've canoed on lakes with heavy fog. Maintaining a straight course requires a compass (easiest) or long piece of cord and a float. (By streaming it behind you and keeping the wake of the float centered in the wake of the boat, you can keep a straighter course.
Conditions that produce fog often have a layer of cold air near the surface. Since the speed of sound is slower in cold air, sound tends to refract toward the surface -- sounds carry much further.
So some form of sonar may work. Construct the equivalent of the clap board used for syncing sound and action on movie sets. The idea is to make a single sharp sound that is uniform.
If you have two people, one person can construct ear funnels out of bark to make hearing more acute and more directional.
If there is any surf running at all -- even light swells -- these are generally going to run toward the main shore -- within the 180 degree angle of the mainland. This assumes a linear mainland with a sloped beach. Such a beach can't act as a source of waves. Cliffs however can reflect waves.
Waves hitting the shore may make enough noise to be heard from a distance, especially with treebark sound amplifiers.
Because strong waves can't come from the mainland side, you may find that there is a difference in the evidence of wave action on different parts of the island. I would expect the dominant signs to be in the direction of the dominant winds for your location. Things to look for: Driftwood, seaweed further up the beach, larger sand grain/rocks (bigger waves move bigger stuff)
If you know what direction the land is, but don't know where that direction lies, you may be able to tell at sunrise or sunset. (That is, you know that the land is East of you, but which way is East?) Unless the fog is extroidinarily thick, you may be able to see a general lightness in one direction. If it gets brighter, as it fades in directionality you 've seen sunrise.
When fog is dense it is frequently in thin layers. Depending on the shape and vegetation of your island, you may be able to climb high enough to see.
If you know the local currents and tides, you may be able to pick up their directionality by running floats on cords from the island. Unraveling your sweater is a source of cord. E.g. You know that the rising tide has currents from the Southwest. You can tell if it's rising by putting markers on the beach.
If the tides have a significant rise and fall, your 400 m to the beach can be far less at low tide. E.g. In the Georgia Straight between Vancouver Island and the coast of BC tides run 30 feet. At a 1 in 10 slope, that chops 300 feet off of each end of your journey. Your 400m is now 200m. Maybe now you can hear the waves lapping.