French citizen apply Chinese visa in Wellington?

Generally speaking, the applicant should be in New Zealand when the application is lodged. You may contact China embassy in Wellington to see if you can have your husband to submitted the visa requirements for you and your daughter as the embassy is the nearest one to New caledonia.
You are required to submit: passport, one recent passport photo, visa application form V2011A and V2011B; previously used China visa; invitation letter from relatives, friends in China, including the inviters' personal details and contact information and probably air ticket.
Besides these documents, you may need to submit the additional documents for your daughter if this is her first time to China: copy of your daughter's birth certificate, copy of the parents' passports (information page only) and valid New caledonia visas page (if applicable).