That form seems to be what's needed to get a French PPL based on your New Zealand licence. I'm wondering if you would need that, as you already have organised a UK (or Part-FCL) PPL equivalent. Flying a G-reg aircraft to France on a Part-FCL licence would only require you to go through the normal flight planning steps and comply with customs and border crossing requirements. I think that you need to find out if your UK validation is usable in the UK only, or whether it will be accepted as a Part-FCL licence, in which case you can cross most EU borders without too much fuss. Keep a wary eye on the Brexit proceedings of course, as that may change things.