The choice of distilled water in particular for a historic recreation is very strange; water makes a big difference. Unless there's reason to believe water in whatever part of France is very soft, a bottled spring water would have been a better choice if you don't want to use tap.
Right, simple minerals such as calcium can make a big difference in final taste of a beer. The excess calcium in waters of karst country (big limestone deposits) is said to have a huge effect on German beers historically, and I'd imagine some of that extends into France as well.
Distilled water minimizes variables of course, but it by itself indeed very non-historic.
