you never mention if your bike has drop bars or flat bars - the Fuji Regis nowadays is a cross/comfort bike with flat bars. but based on the sound of things, your 1985 model has drop bars.
you'll want to disconnect the brake cable (preferably the front brake, since that will be easier for you to work with) and then you either will have an allen screw or more likely a flathead screw inside the lever body, visible and accessible when you pull the lever against the handlebar drop.