I will be flying to Paris on Delta and arrive at 7:55 am, my next flight will be a British Airways 12:10 flight to Heathrow. These flights were booked separately, do I need to go clearout of immigration/customs and go to BA desk to check-in or can I pre-print my BA boarding pass and go directly to BA board gate like I would on a connecting flight??
Since you're on separate tickets, you will need to go through immigration and customs on arrival at CDG, then make your way to your next gate, passing through security on the way (since you will have left the secure area). If you have checked luggage, you will have to claim it before going through customs, and recheck it with BA. If you don't, and you have your boarding pass for your BA flight, you should be able to go right to the security line, without having to stop at a BA desk.
If your arriving Delta flight is on time, this won't be a problem. If it's delayed...
Delta lands at terminal 2E; British Air departs from terminal 2C. For more details of what's involved, the Easy CDG site is helpful. Here's their connection page, but do note that they emphasize that their suggested connection times don't apply if one is flying on separate tickets: http://easycdg.com/passenger-information/connecting-flight-connections-paris-cdg-airport/where-to-go/
What Harold says sounds right to me. You basically have to "arrive" in Paris, i.e. go through immigration and customs procedures and go out into the arrivals hall, then go to the other terminal and find your next flight to check in to.
If your Delta flight is on time, this should work. If it's any more than an hour late, you may run into difficulties. Hopefully all will go well.
We passed through CDG in january 2017 on separate ticket to Rome.
Upon arrival in CDG we went through passport control on our way to the terminal of our next flight and got stamped and then went to checkin kiosk printed boarding pass and through security screening for the connecting flight.
Checkin for BA is in Terminal 2C
CDG is, in my experience, a well run airport. The French are very efficient.
Given your four hour layover time you should be able to get through everything, even if you make a mistake along the way. And have time for a glass of good French wine and a pastry. Enjoy your trip.
Spend some time between flights (if you have time) at the caviar bar.