There are several possibilities as to what's causing the poor fruit set, and the factors may be overlapping or cumulative. Insufficient light is often a key reason. If the trees are not in full sun (8+ hours of direct light daily in summer) or are competing with each other for resources (light, moisture, nutrition) then that may suppress the production of flowers or fruit. Both of these varieties are noted to have above-average sensitivity to late spring frosts, so if flowers were open during a freeze, they may have been too damaged to support cross-pollination and/or fertilization for fruiting. Sometimes an overnight frost will kill pollen without ruining the rest of the flower itself. Bees will also not be flying if the temperatures are too chilly or rainy during the blooming period. (Plus, insecticide use must be avoided during this window. Not only can they harm pollinators, but some will cause phytotoxic damage to the plant itself.)

Otherwise, 'Fuji' and 'Granny Smith' should be compatible in terms of pollen and bloom time. (There are several strains of 'Fuji', though, but we see no indication any of them would be significantly different with regard to compatibility.)

If the trees have been trimmed (aside from the small area where they're overlapping canopies now), this could be forcing them to stay in "juvenile mode" and not mature enough growth that would be producing fruit. Overfertilization, especially with nitrogen, would also stimulate a tree to forego fruiting in favor of foliage growth. If the trees' root systems grow into surrounding lawn, the lawn fertilizer may be contributing a sizeable proportion of nitrogen depending on what was applied.

Have the trees been treated with preventative applications of pesticides (organic or otherwise)? If not, stresses or damage caused by pests or disease over the course of the growing season could also be directing the tree's resources away from fruit production, or may have caused flowers or young fruit to abort due to stress. As with ornamental plants, flower/fruit drop might also occur as a result of drought stress or over-watering if your client is managing the tree's care day-to-day.

You may have already seen our apple care pages, but in case not, here is a link, if useful. Note that the bottom of that page contains nine additional links to content regarding apple (and general fruit) cultivation and pest/disease management.

Miri