Paris on Easter Sunday

I suspect the churches will be filled with people attending religious services and not available for 'tourists'

If you are looking for a museum or such, I would definitely contact it to confirm if open and what hours.

Even Costco is closed on Easter, Thanksgiving and Christmas

Tourists come and go through all the churches, even during Mass. It's a shame.
There is usually a sign "Messe" at Notre Dame, on the left door, where you can go to celebrate Mass. You just walk right in, no problem. Go right up front and sit down.

I don't think you need to worry about any areas being avoided.
Just check the official websites of whatever you want to see, for opening hours.

I suspect the churches will be filled with people attending religious
services and not available for 'tourists'

Perhaps tourists can turn into VISITORS and attend the Easter service. Talk about experiential travel. It's the most celebrated mass of the year; everyone of course is welcome and the music will be sublime.

We were there at Easter a few years ago, I don't remember any sights being closed, but some restaurants were booked up with families enjoying a special dinner.

Churches, at least the ones that attract visitors, should be open for visiting as well as worshipping. But good advice above to attend mass if possible -- a time-intensive but rewarding "back door" experience.

Easter In Paris: https://en.parisinfo.com/discovering-paris/major-events/easter-in-paris

Easter 2017: http://www.parisinsidersguide.com/easter-in-paris.html