Chicago Dublin Paris 2 flights or multi city?

Will I need to go thru customs, retrieve my bags, and check in when I
arrive in Dublin from Paris before going on to US?

Yes, since this will be two separate tickets.

Any chance Aer Lingus will allow me check bags through to US when we
leave Paris

Probably not, airlines have become very reluctant to do that. But, you have nothing to lose by asking.

or should I have gotten multi city tickets?

Yes.

I agree, probably yes to the last question. But the silver lining is that DUB has US passport control and customs, so when you board there you're effectively on a US domestic flight. That means you'd have to handle your bags there even if you were on one ticket homeward. So the added hassle of going landside to retrieve them might not be as bad. If Aer Lingus, is waiving change fees (as many airlines are now), maybe you could still do this on one ticket, and maybe even without that Dublin connection. Or maybe the time saved with a multi-city booking is worth the change fee, if Aer Lingus can fly you straight home from Paris.

If all your travel is with the same airline it may be worth checking the fare for the multi ticket (for Aer Lingus it is called a stopover itinerary). You will need to call their help desk for this type. Sometimes it may be more expensive. If it’s a bargain (including any potential change fees) then go for it. If not you’ll probably be taking that long route to pick up your bags in Dublin and circle through checkin, security, etc. Like the previous poster mentioned it’s worth asking but doubtful. Good luck and have an outstanding trip.

As a PP noted, as currently planned your return flight requires you to clear US immigration in Dublin. Because you are on two tickets, on the inbound flight from Paris you would go through Irish immigration, exit the secure area, claim your baggage, then go through security twice, once for Ireland and then again for the US. You would then go through US immigration. Aer Lingus recommends you allow 3 hours for that (unless you have global entry) and that excludes what ever wait time you might have at Irish immigration.

You should try to can change your ticket.

Update: I wasn't able to change my flight so I booked a separate flight, same airline, with a 5 hour lay over. It'll be an incredibly long day, but I think 5 hours should be enough to get luggage, get through customs, and check back in. (Fingers crossed)