Preheat oven to 350°F.
Clean the zucchini without peeling them.
Slice the zucchini and cook them in salted boiling water until tender.
Meanwhile, peel the onion and cut it into thin slices.
Drain the cooked zucchini, reserving 2 cups of the cooking liquid.
Gradually combine the reserved liquid with the beaten eggs.
Season the egg mixture to taste.
In a large casserole dish, alternate layers of cooked zucchini, sliced onion, sliced cheddar cheese and French-fried onions, reserving plenty of cheese for the top.
Pour the egg and zucchini-liquid mixture over the casserole.
Top with the reserved cheese.
Bake uncovered for 1 hour, or until the cheese is well browned.