Two separate tickets for two separate flights

You will go through immigration in Paris, collect your luggage, go through customs. Then you will be outside of the secure area.

You then go to the airline desk and check your luggage. Then go through security and immigration.

I would allow at LEAST 4 hours to do all this at CDG. If you miss your second flight, you buy another ticket last minute. The airline has no obligation to honor your original ticket.

small regional airlines are often not all that reliable on times. You might look at the record for your first flight as you have a catastrophe if you miss the second. I would not schedule this with fewer than 6 hours between. It is always risky. We almost missed a flight to Rome because our 6 hour layover was eaten up by problems with the first plane. That was on one ticket so we would have been covered but there are not always places on the next plane. Doing this on two tickets I'd build as much grace in as I could.

As someone who does a lot of non-protected connections, I’m doing one going to Europe next month, for example, You have to be willing to accept some risk to do this

And the less risk you are willing to accept the more time you need to allow. So in your case, if you missed that second flight, the second airline owes you nothing and even if the first airline is liable under some government regulation it is probably not going to be enough to buy you a new ticket to Tokyo. So in that case, I would want a lot of time. For me, this would be a fly into Paris, spend the night at the airport and go out the next day. That’s what I always do if I am connecting in Europe to fly home, for example. I get to the city where my plane leaves out of the night before. Airport hotels are often not outrageously expensive so it’s worth it.

Self connecting through CDG with passport control both inbound and outbound, you will want no less than 4 hours between flights, 5 would be better.