Schengen still exists and operates like it did before.
But certain (very few) French airports were requesting advance details for intra-Schengen flights. What you need to do is check the notams for your intended arrival airport. If it has extra procedures notified there (or in the AIP) then comply with those, otherwise it's no notification as normal.
When it comes to leaving the Schengen zone, you'll find far fewer airports in France with customs facilities than previously available.
I have a memory in the back of my mind that Greece basically ignores the Schengen agreement and demands entry and exit via a customs airport, irrespective if it's to/from another Schengen country or not. But I could be wrong on that.
A tip for Greece. If you are an AOPA member, bring your membership card, as there are significant discounts on the handling fees for AOPA members. It might even be worth your while joining just for the trip, depending on what Greek airports you're using.
dp