I think we should start a 'My ex is a bit of an arse' club as we seem to have plenty of potential members on here.
Glenda has put a useful post on
here so I don't know if you will glean any help from that.
Unfortunately, if you do need him to sign a letter and he won't, I guess court action is the only solution. I don't really know how you stand with already living in a different country with your daughter and whether it changes the rules in any way. NZ is a bit of a stickler with getting the documentation just right when a child is being removed from its base country so it wouldn't be the case that you could wander in like you did in France.
See what you think about the article in Glenda's post and how it applies to your particular case. If you feel you will need a letter to be signed by the father, the only thing you can do is prepare one and submit it to him, possibly by way of a solicitor if you don't want to tackle him yourself. Perhaps he'd find it more difficult to refuse a legal body than he would if you were to do it. He might enjoy jerking you around for the fun of it, but he wouldn't get the same pleasure with a solicitor. Might be worth a try. Good luck.