As far as I am aware no French prisoners were held at Lymington. The story that they built some of the walls in the area is a local myth, as POWs were not used on construction projects as it took work away from the civilian workforce. The nearest prison depots would have been Portsmouth, or the parole depots further north in Hampshire.
However, it may be that Louis Le Blanc was a Frenchman who settled in the area after the war was over in 1814. Or, as Lymington was a base for the King's German Legion it could be that he was recruited into this force from one of the prisons and settled here. The KGL recruited extensively from amongst the prison population, but were not allowed to recruit Frenchmen. Many thousands of Germans were enlisted so could Louis be German?
Hope this information is of use, and good luck with your research.