Is your wrist dropped when you're playing FH? There should be a straight line from your arm to your bat, i.e. your bat should be pointing sideways and not UP when you contact the ball.
If your wrist is not dropped you will never be able to relax.
Also the grip is important. Try to shift to a less tight grip by shifting your hand downwards relative to the blade face.
The next problem is using arm only strokes. This will definitely cause you to have a tense stroke. Use your waist rotation, and weight transfer + pushing off your right leg for power, not your arm.
Once you done all the above, I'm quite sure if you have a correct stroke, you will have a relaxed grip.
One tip after mastering all this. Let your index finger rest on the rubber, not pressing it, you can even have it leave the rubber for a while, then when you're hitting the ball, use your index finger to give the blade a nudge forward. This resulted in a MASSIVE increase of power and relaxation for me. But it's not recommended for beginners :P