I'm confused... Why not just write it as if you were writing about everyday, deterministic life?
Well, the original influence of this being the case, was a dream I had the other night where a character said "We lost our freewill years ago". But writing it as how it is is sort of dull, so I plan on using the common understanding of freewill according to believers in it.
I'm also rethinking about actually making freewill a human invention that ends up causing too much chaos and so it was banned and now people that are used to living with freewill (it lasted atleast two generations) are struggling to exist in their limits as they're simply not used to it. But they pretty much gotten used to it (to make the story itself actually speed up a little without the struggle of living determined consuming most of it), but there are a number of people that do still have freewill, or have illegally used past techniques to get freewill.
Beyond this, I'm not going to let this drive the plot. It's just going to be their environment, how their world is, but there will be an event based in the world with this features. It will effect plot a little, but not by much.
A few ideas that I had in mind were: People without freewill still had the (artificially created) gene of freewill that made them see through a freewill perspective while engulfed in determinism - so they are sort of claustrophobic with these limitations.
They will go about similarly as we do now, but their freewill-perspective will make them not have the illusion of freewill, they'll actually feel the determinism.
Humanity is much more safe because of its restrictions but freedom wasn't a feature.
Freewill people will have the struggle of having freewill in a deterministic universe. Not much of a struggle, in fact a benefit, they can practically change the determined course of the universe to a certain extent.
Freewill people try to live their lives normally and attempt to blend in, but it isn't easy.
The world with freewill was more free and unlimited. But safety wasn't a feature.
Freewill people basically seem like us, until you pay close attention you will notice some things that seem paradoxical or impossible.