You can't use a GFI on that unless you rewire it if I understand the situation properly. What I think you have is what is referred to as a shared neutral. It is coming off of a double breaker. A double breaker can also be used for a 220vac circuit. Your house has 220 coming in, and the neutral is tapped on the transformer half-way across, so if you measure from one side or the other to neutral, you get 110. When wired this way, because the two hot legs are on the opposite side of the transformer, the current going back through the neutral from one hot will be positive when the other side is negative, and they cancel out. This allows you to save a little bit on the wire - using 3-wires, you get two 110vac circuits. Since the current cancels out, that neutral will never carry more than the current that is on one leg. Since a GFCI needs a dedicated neutral on each leg, it will be unbalanced most of the time and therefore trip.