Q: Is the AirPort Express Fiber Optic compatible? (Verizon Fios)

The Airport is a router, not a cable modem. Verizon are presumably supplying a cable modem which is also a router, and so has an input for the cable lead and several ethernet outputs; it may well also have wifi.

You can probably turn the wifi off if you would rather use the Airport; and there's nothing to prevent you connecting the Airport's input to one of the Verizon's output ethernet ports and using its wifi. As long as it's a reasonably recent one it should detect that it's connected to a router and configure itself appropriately.

We need to know the make and model number of the modem/router that Verizon will be supplying to you.

The fibre connection usually comes into the house  either as an actual optical fibre or as a coaxial cable carrying the data converted from fibre in a box in the road.

It needs a 'modem' to convert the incoming data to an ethernet socket (the same as you your Mac's wired network connection). This can be just a box which does that and no more, and has only one ethernet output, or more usually it also includes a router (for sending the data to the particular device which requested it) with several ethernet outputs. It will also often have wifi, so it can be if you wish used without any further routers.

The Airport express has only an ethernet input and so cannot be connected directly to the incoming fibre or coaxial cable. It can be added to a cable modem/router to provide the wifi connection.

If you are interested.......We can tell you more about compatibility if you can furnish information about the make and model number of the modem/router that Verizon is providing.