If space isn't an issue (i.e. lots of acreage), how many chickens make a happy flock?
What is your definition of a "happy" flock? I'm looking more for a contented flock, one where they are not fighting or brutalizing each other. But that is just semantics. Mine get to live life as chickens. If they free range they will let you know what works for them. With enough chickens and enough room they will form sub-flocks and cliques. Roosters often claim their own territory. Some hens will stay with a specific rooster, call it a harem. Some hens may wander around on their own, at least part of the time. Some of the hens in a harem may not show any loyalty to that rooster if an opportunity arises. There is no sweet spot that works for everyone, it's whatever works for you.
I am looking to free range and breed chickens on the land. (Cream Legbars, Bielefelders, and American Bresse)
Then you can't free range them all the time and keep the breeds pure. You will have to set up breeding pens to keep the breeds from crossing.
I've read that about 50 chickens can free range on an acre without killing the soil from too much nitrogen,
You can read a lot of things, some of it might be true. A lot of this will depend on your climate and time of year. Some on your native plants. My area for chickens in Arkansas was less than 3000 square feet, less than .07 of an acre. My wintertime laying/breeding flock was just one rooter and 6 to 8 hens. During the summer I'd have over 50 chickens on it at a time, most of them chicks growing to butcher size. The soil was not killed by too much nitrogen. There were some bare spots, mainly around feeders and waterers and where they like to take dust baths or under brush where they liked to hang out. They did selectively eat the plants they liked and avoided the ones they did not so I had to mow that area a few times a year to allow the good stuff to grow. In the spring I locked them up for about a week when the green stuff started to grow to let it get established, that was with very few chickens at the time. I did have fruit and nut trees in that area. The trees did not die. The chickens did not die from eating fallen fruit.
How many chickens an area will support depends a lot on the time of the year and your climate. Obviously they can't forage much if the ground is covered with snow. Rainfall has a lot to do with it. An acre in a moist climate with warm days so stuff can grow can support a lot more chickens than an acre in a desert. Some seasons are warmer or wetter than others.
If you let them roam that much area I don't think nitrogen overload is even close to being an issue for you. Predators can easily be an issue, probably will. Where are they going to sleep at night? Trees, one big coop, or will you build individual coops and shelters and train them to use them? Where will they lay eggs? How are you going to feed them? I think you are worrying about the wrong thing.
is it better to keep flocks small and segregated? My thinking is that by separating them into smaller flocks, they may have less issues with disease and pests.
As I said above, they will manage flock size in how they hang out. Unless you fence them in you won't have any real control over that. But that is a good point. The higher the chicken density the more the poop builds up. The more the poop build-up the more diseases and especially parasites can build up. This is much more of an issue if you keep them in runs and a reason you need to manage poop build-up. Spread out like you say they will be this isn't much of an issue for you. Other than where they sleep the poop load should be really light.
Dad kept a free ranging flock that usually consisted of one mature rooster and 25 to 30 hens, with the numbers going up when the hens hatched chicks in spring and summer. They'd roam maybe 2 to 3 acres, much of that under fruit trees. He did not feed them in the good weather months, they fed themselves. But, and this is a big but, they had high quality forage. Not just plants but we had cattle and horses which generate additional food for chickens. They caught a lot of creepy crawlies and insects. In winter he did feed them. You have to remain flexible and react to your conditions and what you see. What I saw with Dad raising them is what I'm basing a lot of this post on.
I think you will have a fairly steep learning curve. I think the issues you have are not what you are worrying about now, you have to stay flexible and learn. I don't know where you are located so no idea of climate or foraging capacity. I don't really know your goals or how you plan to manage these chickens. My main suggestion is to get started, maybe with less than what you think will be your maximum number, and pay attention to what you see.
Good luck!