New Zealanders aged between 18 and 30 can apply for a 12-month working holiday visa for France.
Information on the application process can be found on the the official visa site for France(external link).
Three-month visa-free access (as a visitor) immediately following the expiry of a Working Holiday Visa is not an automatic entitlement. Working holiday visa holders are required to leave France before the expiry date of their visa. Re-entering soon after the expiry date as a (visa-free) visitor is subject to French border control. The reasons/bonafides of a quick return to France may be questioned as Working Holiday Visas enable holders to both work and visit for up to 12 months.
Advice for New Zealanders who wish to travel in the Schengen Zone can be found on the Safetravel website: Travel tips for Europe(external link).