I haven't been to PTP in a few years. However, when I flew FDF-PTP-MIA the FDF-PTP flight forced all passengers landside. Same thing when we arrived the other way from the US. They specifically collected us passengers connecting to MIA and took us back in airside with an escort. So you may find that you are forced landside and through immigration. You'd then need to go back through security and exit immigration. It's a relatively easy airport, so as long as you have enough time it should be doable. Are you on one ticket?

Also the AF lounge in PTP was windowless as I recall, but the AC worked and it had a decent enough spread of wine and snacks. The Priority Pass lounge mentioned by the poster above looks like it might be better though.