The Bairns enjoyed a profitable first season back in the Premier Division, challenging for European qualification and eventually finishing fifth, only six points behind 2nd place Motherwell.
In July 1995, Jim Jefferies resigned as Falkirk manager to take-over at Heart of Midlothian and Fulton was one of the first players he signed for the Edinburgh club.
The side had been near the bottom of the table at the time Fulton signed but recovered to finish 4th and reach the Scottish Cup Final, where Rangers proved too strong for them.
[5] Due to an injury to regular skipper Gary Locke, Fulton was appointed captain for the occasion and he set his side on the way to victory after he was brought down in the box to win a first minute penalty kick from which they took the lead.
Jim Jefferies was by this stage Kilmarnock manager and he again moved to sign Fulton, offering him a two-year contract with the Ayrshire club.