The English word was JADE (the French was DEJA). If the four numbers are W, X, Y and Z and their total is T then

(W + X + Y)/Z = (T - Z)/Z

Since the left-hand side of the equation is a whole number then both (T/Z) - 1 and T/Z are also whole numbers. By symmetry, W, X, Y, Z are factors of T. The possible factors of 20 are 1, 2, 4, 5, 10, 20. The four of these that sum to 20 are 1, 4, 5, 10. Replacing these by letters gives A, D, J, E.