How is fuel managed in the Zero-G A310? There are several Zero-G airplanes to experiment briefly microgravity without going into orbit. One is the A310 from Novespace (F-WNOV):


Novespace A310 F-WNOV (source: Jonas Wirz at Airplane-Pictures.net)

When a Zero-G flight is executed, fuel should take the form of a sphere in the tanks, like demonstrated in the cabin for a beverage.


Advertisement in microgravity (source)

Thoughts:


This effect won't appear in negative G, subject to the design, fuel lines may still be immersed in tanks, this cannot be the case in micro-gravity. 
The 0G segment is likely flown with power. First this is not a continuously descending flight as seen below. Second, friction will slow down the free fall anyway and must be compensated by some acceleration from the engines.


0G segment is not limited to the descent (based on source)


How does Airbus ensure the fuel is still delivered to the engines at the required pressure, without air?



Related: Are engines fed differently in reduced gravity aircraft?

Basically it says no modification is required because the lines are pressurized, and this is supported by a 1966 Nasa study (Use of aircraft for zero-gravity environment) which is not more detailed. The line being pressurized downstream of the pumps seems only one element of an adequate design. Upstream fuel will experiment the effect of micro-gravity and lines are no more immersed in the fuel. Air can enter and create a problem when reaching a pump or an engine. Pumps could be drained. Maybe the problem won't appear during the 0G segment, but it should appear later.

I'd like to have the details about how pumps, pressure, flow, or anything else contribute to maintain a good fuel supply to the engines.



This is the fuel system for the A310:

  

(Source)
I wrote an email to AirZeroG and asked them:


  Other than the interior, are your aircraft modified in any way to handle zero-g flight?


Here is the response that they gave me:


  Dear Sir,
  
  Except free floating area cabin configuration, there are very few differences with a “standard aircraft”. The most significant one is installation of Zero-G meters in cockpit and a very simple installation on the wheels to help one pilot to lead the aircraft only in vertical axis, and the other pilot to lead only in horizontal axis.
  
  Out of that, the biggest difference is maintenance program: each parabola performed to create Zero G onboard is considered as an aircraft cycle for the aircraft and its engines, and maintenance adjusted accordingly. Such consideration dramatically increases maintenance costs of the aircraft.
  
  Kind regards
  
  Gilles GOMPERTZ


I would say that if there were a fuel system difference they would say that is more significant than G-Meters in the cockpit. I'm assuming based on the response above that the fuel storage/delivery system is unmodified.