No to CPS that just fine tunes fuel injector timing, and not used at startup.
Is it hard to start anytime or just when cold or just when warmed up?
Before starting turn key on and count to 3, then turn key off.
Then repeat that 2 more times
Now try to start.
If it starts quickly every time after doing this then you are losing fuel pressure somewhere.
Fords fuel pump only runs for 2 seconds when key is first turned on, from 0 pressure that will give system about 15psi of pressure, normal pressure is 60-70psi.
So repeating 3 times should get you up to 45psi which is close enough to start engine.
Another test is to get some starting fluid(ether) in a spray can.
Before starting pull off Power brake booster hose and spray some into the intake, put hose back now try to start.
If it doesn't fire then spark is not coming on, that could be a CKP(crank position) sensor issue, BUT(big but) these are not the king of sensors to be intermittent, I would expect a no start, until it was fixed, not longer cranking.