How to bind key to search for a file and paste the path to the command line?

[Marcin Barczyński]

fzf (https://github.com/junegunn/fzf) is a program that let you find things
easily and prints the selected item to stdout.
For instance:

$ find . | fzf
/home/user/a/script/very/deep/in/the/directory/tree/foo

To make my life easier I would like to bind Ctrl-F to run "find . | fzf"
and insert the path at the position of cursor:

$ cat <Ctrl-F>  # runs find . | fzf
$ cat /my/script

How to do it in bash?
I tried:

$ bind -x '"\C-f":"find . | fzf"'

but it prints the path to stdout instead:

$ cat <Ctrl-F>  # runs find . | fzf
/my/script
$ cat

-- 
Best Regards,
Marcin