Comment # 1 on bug 1225278 from Martin Sirringhaus

Can confirm. The logs say

gnome-shell[2546]: Received error from D-Bus search provider firefox.desktop:
Gio.DBusError: GDBus.Error:org.freedesktop.DBus.Error.ServiceUnknown: The name
org.mozilla.Firefox.SearchProvider was not provided by any .service files

I think we have to update our desktop-file and install the service-file, too.
See https://hg.mozilla.org/mozilla-central/rev/cec10bb1eb83

I'll experiment with it.