The simple part of this is to add a "No Internet" banner to the top of the "Latest", "Categories", and "Updates" screens. The more complex part is that when viewing an apps details while offline, it will present the user with the option to "Download later". This stores a flag against the app in the database, so that whenever they visit the Updates tab, it will show a list of apps that have been marked for subsequent download. These will then automatically download next time F-Droid receives a network connection.
There are likely a handful of edge cases when this will need to be ironed out, but for the most part, it is a fully working feature.