I am flying from the UK, connecting in Paris/CDG for an international flight to the US: Newark NJ. From there, I fly to Savannah, Georgia and on to Lexington, Kentucky.
I am a British citizen. Do I need a visa for the CDG connection?
As has already been said, you're not going to need a visa (although you will need to pre-register through ESTA) - but whatever you do, do NOT book this itinerary.
The problem with some online booking engines is that they will put multiple flights together without knowing the implications of doing so. In this case it has given you 2 legs on Allegiant airlines - Newark to Savannah, and Savannah to Lexington with a one hour connection between them. EVEN ALLEGIANT THEMSELVES WILL NOT SELL YOU THIS CONNECTION. It is, very simply, not possible.
Allegiant is a low-cost carrier, and they do NOT offer "connecting" flights. Thus these two flights are considered two individual, single-segment flights. After you get off the plane in Savannah you will need to collect your bags, then proceed to the check-in counter to check in for your second flight, pay (again) their checked baggage fees, and then get through security to your plane. All within (less than) 1 hour.
If (when!) you miss your connection, Allegiant will not offer any assistance - as they don't sell connecting flights!
If you have no checked bags this MIGHT be possible (if only because it's likely the same plane flying both flights), but again if anything goes wrong then you will be on your own.
You're flying from the UK, connecting in Paris/CDG for your international flight to the US/Newark NJ. From there, you're going to Savannah, Georgia and on to Lexington, Kentucky.
As an EU citizen, you don't need a visa, transit or otherwise, to connect in Paris. If you already have your ESTA for the US (or visa, as appropriate), you clear customs and immigration on arrival at the airport in Newark (EWR), entering the United States, and go to take your domestic flights.