Just do the conversions when the property changes hands. The new deeds would have the new measurements. It wouldn't need to be done overnight, and converting every parcel of land in the country could take a couple of generations (land doesn't necessarily change hands every day).
If I were to give half my farm to my son, we would each have 80 acres under the confusing old English system, but 32.374851 hectares under the French system. A subsequent division would yield 40 acre farms under the English system or a far easier to work with 16.1874255 hectares using the french system.
You got me convinced.