Welcome Rob, an electrical expert will be along soon, but in the mean time, trying to get my head around what you have said.
I believe you have a booster/charger set up. This feeds the battery that then feeds the lights. Feeding the power through the battery smooths the supply to the lights and they are less likely to flicker. This is particularly the case if running LED replacements to the standard fit halogen, that burn the top of your head.
The battery should charge when connected to the mains, so I'm guessing some switch needs to be flipped.
As regards blue and brown swap over, welcome to French electrics. On 230v this is fairly common, they did not worry.
On 12v blue is +ve and brown is -ve, don't ask me why, it does not make sense, it just is.
Colin