Meeting travel companion in Frankfurt airport.

I would definitely go on and get the bags. Leaving them unclaimed for two hours might result in the airlines putting them somewhere else if they go unclaimed that long.

If you are arriving from North America, you have to get your bags and got through customs, which should entail just exiting baggage claim through the green "Nothing to Declare" door. So if you don't pick up your bags right away, you will not be able to get back into the baggage claim, since it is exit only. Your bags will probably be impounded if they sit there very long, and I am sure they are going to want to take a close look at them since you suspiciously did not claim them right away.

I would not recommend staying in the arrival/gate area to wait for your companion while your bags go around on the conveyer belt only to get removed by an airport employee and taken to lost bags. Instead move on through customs and wait in the exit hall at a coffee shop or meeting place. Will you be able to text the location of the place you are waiting to your companion once you see a convenient place and are settled there waiting 2+ hours for them?

Get your bags and then go to a cafe, and later sit at the Meeting Point to wait for your friend.

Always get your baggage.