How to map media keys to "short jump" in vlc?
Actually mapping any key in a specific application is built into macOS.

system preferences > keyboard > shortcuts > App shortcut

Once you are there click the + and select VLC from the Application menu at the top, then type in the EXACT menu name. Exact is important it has to be capitalized correctly and if it has "..." at the end remember that is not three periods its an ellipsis which you get by pressing Option;. Then click in the Keyboard Shortcut field and tap the key you want to assign. In your case that would be F7.

This can generally be done for any Application that does not have a keyboard shortcut already assigned. If there is one already assigned you may have to remove that first.