That may be working aganst you. Im always stronger when training my triceps after having a good biceps pump. But if you arms arent big enough for this to matter, it wont matter
If youre a triceps dominant presser than you dont need to do extra pressing for triceps. There are no rules for this.
The pressing and regular extension/pressdown are going to hit the same two heads really. Its the long head thats hard to target without doing a movement from a stretch position. PJR pullover is superior to overhead french press IMO.