DTV is a multiple entry visa valid for 5 years. You don’t need a re-entry permit to leave and return. It’s built in to the visa. Every entry grants you 180 days.
France uses the evisa system. Fees are payable on application. If rejected there would be no refund.
Almost certainly you’d need to pay the Muay Thai place upfront. Although that’s probably specific to each embassy and I couldn’t advise what Paris requires.
Paris is well known to take a long time to process a visa. Like a month or so.
If you are not close to the airport where you entered you could try going to your local immigration office to see if they will correct the stamp for you. If not you’ll have to travel back to that airport and have them fix the stamp.
It’s going to cost you $800 per person to get a Non O visa in NZ or $2,000 per person for a Non OA. Absolute madness.
Save that money and arrive visa exempt. Spend a few thousand baht with an agent to open a bank account (you will find it incredibly difficult to do yourself).
Once you have the bank accounts then put in 800k in each account and apply for a in country Non O for 2,000 baht. When that’s winding down apply for the year extension for 1,900 baht.