I found, and fixed, a couple of things in the AI that prevented it from making units but I still don't really know why it is building so few. My main suspicion is that it is mostly because in FFP, unlike FF, the AIs can actually build things on all of the planets when in FF the only place it ever changed what the build planet is happened in the Python AI overrides (in the function mentioned in the next paragraph). Because of that, regular FF runs out of buildings to build and then builds mostly units (or occasionally research or whatever) but it takes FFP much lonver to run out of buildings whcih can be built in a star system. The most puzzling part is the basic defense. That was bumped up slightly (as I recall it is having it round fractions up instead of down, basically, so in either the the 2nd and 4th eras or the 1st and 3rd eras, I don't remember which, it wants 1 more than it used to) but it still does not seem to want to build the specified minimum even though the code in the DLL should be making it do so unless one of a very few high priority things overrides it in there. And yet it doesn't seem to actually do so all of the time. I did not walk through that code using the debugger during a game enough to see what the problem was.
It is possible to make it the AIs build units via Python. In the CvAI.py file the doCityAIProduction function is overriding the AI in some specific ways when it is starting the build decision making for a city. Almost all of what is done in that function involves making it build buildings to solve specific problems (like building a sports arena if it is at or very near the happiness limit, for example). Originally the only units it built were construction ships. Now it can, in recent versions, queue up a few military unit types: carriers and squadrons. It won't have a city build any other unit types.
There is an even easier thing to try adjusting. In the XML it might help to increase one of the settings in the CIV4LeaderHeadInfos.xml for all the leaders. Each leader has a value called iBuildUnitProb. Currently the barbarians are at 50 and the real civs are in the 20 to 40 range. Bumping these up some more might help a little (they were all increased by 5 a long time ago). Another 10 or 20, or maybe even 30, added to each of them might help. I do not expect this to solve the problem, but it would probably help some. It may also help to adjust some of the parameters relating to planning wars, to make it more likely. These are the iMaxWarRand, iLimitedWarRand, and iDogpileWarRand - for these a lower value makes them more likely to want to go to war so subtracting 5 or 10 from each (or maybe a 10% reduction to the current value for each) could be interesting. I seem to recall there being a dividing line at 100 where going below that value triggers some other stuff too. Unfortunately adjusting this could have them endlessly planning for war without ever actually declaring war, or even worse just going to war a lot without being more prepared, instead of actually making them more aggressive in a way that makes them more dangerous.