We are arriving into Frankfurt from US next month in the late afternoon. We are booked ( via our airline tickets ) into Stuttgart via rail for the final leg of that trip. We however, would like to consider leaving directly from Frankfurt enroute to Belgium straightaway, rather than arriving in Stuttgart and leaving the following day for Bruges where we're booked the following evening at hotel.

Can anyone advise us to either take a train directly to Belgium from Frankfurt airport, or to rent a car there in Frankfurt and set off driving that evening towards Belgium?? Or should we simply complete the airline's itinerary and arrive in Stuttgart the first evening and take a train or car into Belgium the following day?

( We're departing from Stuttgart the following week after a party there for our return to the US. )

Since there will be a penalty fee for dropping off the car in another country than where you rented, the car will only make sense if you keep it until you get back to Germany (Stuttgart, in your case, I assume). If that makes sense and you can use the car to drive around in Belgium, or if the car will only sit in a hotel garage in Bruges for a week, can only you decide.

The train looks like the better alternative.
You can check itineraries at www.bahn.de (language can be set to English)

And I would also inform the airline that you plan to forego the Frankfurt-Stuttgart leg to check if they have anything against it. Which would not be legal here, btw.

I wouldn't drive any distance after a transatlantic flight, especially one which lands late afternoon.
I would say take the train.