Tahiti and Bora Bora are not countries, they are islands in French Polynesia. But yes, FP is not on your list unfortunately.

FP is extremely expensive for cell and data services. Like many Pacific Islands, there is a monopoly on these services. The normal options you might get in most western countries (like Travel Pass, cheap roaming, etc) do not apply.

You should be able to find paid WiFi hotspots around the islands fairly easily, but you'll pay dearly for them. Free Wifi is almost unheard of (at least when I was there 18 months ago). If I recall correctly if you buy a larger package of data (maybe 20 hours?) it was something like $5 US per hour, and the speeds were very slow. If you didn't remember to log out, the hours kept counting. And this is Wifi so you can't be on the move.

If you really must have phone data through the cell network, the cheapest (maybe only?) option will be to get a prepaid SIM and use it in an unlocked SIM card 2G/3G GSM phone. I'm not sure your Verizon phone will qualify. I have an unlocked SIM phone but the prices I saw at the airport made me not bother. I don't recall what they were.

In my opinion, it's best to prepare to be without these services. Load Google Maps offline, this can be a big help. Do as much planning/researching/downloading as you can before you leave. Otherwise just enjoy being disconnected.