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I am from Georgia and have a D category long-term Schengen visa but is marked 01 which means that it's a single entry. Am I able to go from Poland to France by plane?
Yes. You will only be entering Schengen once. When you enter Poland, you are entering the Schengen Area; when you then fly to France, you are moving within the Schengen Area.
You need to enter from the country that you obtained your visa first. After that you are free to go anywhere you want. You can fly back to your country from any schengen country as well.