Making a connecting flight at Tegel airport in Berlin

As always, if you booked both flights together on one ticket, then luggage would be checked all the way through, the flight connection would be "protected" in case of delay, and the transfer timing would be fine.

If you booked a separate ticket from Paris to Berlin, especially on a non-affiliated budget airline, then you probably do have time to go through the procedures above if all goes according to plan but have no protection if the first flight is late. If you miss the US flight, you'd have to buy an expensive new ticket.

Your times above indicate a maximum of 2h 30m, not 2h 40m. That also includes time to get off the first airplane. I'll leave the specifics of Tegel to someone else.

Are these totally separate tickets? If on the same ticket, your luggage will be checked through to the US. So you just have to go through passport check and get your exit stamp and go to the gate.
If not, you are taking a big risk if the Paris-Berlin flight is seriously delayed or cancelled.
Global Entry has no validity except at US Immigration when you land, or at those facilities at Dublin airport.

I'll agree with the points made above about one ticket vs separate tickets.

Tegel Airport is not large, and it's also a ring, meaning that if you keep going around from one gate to the next, you will eventually get back to your starting place. So, at least you won't have the issue of a long time or long distance getting from one gate to another.

Argh! I was afraid I was not understanding Global Entry well enough. Was so hoping this would be enough time when facing 11 straight hours on the plane coming back

Yeah, I think you misunderstand Global Entry. It quickens getting through US Customs/Passport Control. It doesn't count for much at non-US airports, unless they have Preclearance, where travelers essentially go through US Customs/Passport Control in the non-US airport before their departure for the US. Tegel does not have that, which is good for you, because Preclearance would only add to the time you need to be in the airport.

It sounds like you have already purchased the tickets, so the best advice at this point is... Move fast at Tegel!

Air Berlin uses Terminals A, B and C at Tegel. Connecting between these is not particularly convenient.

Noting Mrs EBs first suggestion, you can call AirBerlin ahead of time and ask but this didn't work for us last summer when we did a similar thing, LAX to DUS on one ticket then DUS to Florence on another separately purchased ticket. However at LAX when we checked in the agent there saw our connection time and said she would check our baggage through and combine the tickets and issue a new boarding pass. We had asked politely and she performed a miracle. It never hurts to ask politely at the airport. If they cannot help you with the two separate tickets maybe they can work to seat you further to the front in the plane.

EDIT: another thing that will help your situation is to only have carryons for this trip, no checked luggage. We had one checked bag for out trip last summer because it was a month long and we were attending a wedding too.