You want the find-file-at-point function (which is also aliased to ffap). It’s not bound to a key by default, but you can use
M-x ffap
Or, you can put in your .emacs file:
(ffap-bindings)
This will replace many of the normal find-file key bindings (like C-x C-f) with ffap-based versions. See the commentary in ffap.el for details.