It is very likely a fuel pump problem. It is not really the fuel pump itself, but the inlet screen on the pump module is restricted on your returnless type fuel system. This is very common on late 99 and 00 Contiques and Cougars.
You should be able to confirm the low fuel pressure by driving the car with a fuel pressure gauge attached while it is acting up.
It would not hurt to change the fuel filter just for drill.
The common problem with the fuel pump inlet screen is that it does not have enough surface area or it is just too fine of a screen mesh. Often you can remove the screen and throw it away. You will still have ample pre pump filtering because there is a conventional sock type filter inside that pump module prior to the pump.
If you do a search on returnless fuel systems or perhaps fuel starvation you may come up with a how to on removing the pump without droping the fuel tank. There is more than one that includes photos.
