Unless the water doesn't have the appropriate corrosion inhibitors, like what happened in Flint. Then it'll leech out. It's common that it will be coated in minerals, but it's no guarantee.
It would be very informative to compare the chemical composition of the water in Flint with that as I described in Paris. The immediate observation is that with Flint the Pb was already in the water, presumably with Paris the supply was clean (or comparatively so) and the only chance for it to get into the water would be household pipes.
Clearly the French weren't overly concerned about it. Like most of the EU they overregulate everything and presumably would have mandated the pipes be changed if they thought them a problem.
Or if the corrosion inhibitors actually cause more lead to be leached like the water treatment lab found in Madison, WI, so they rejected the plan and replaced the lead pipes instead