Morten St George Theory

[Paris]

There were apparently no battlements anywhere in France with merlons shaped like sparrow tails. Just google merlons + "queue d'hirondelle"... only northern Italy and Tyrol come up.

I wouldn't say that.
Better say that a few castels in France have (and had) merlons shaped like sparrow tails.

I give you this image from a castle located in south of France, in Cagnes-sur-mer (near Cannes and Nice).
It's the grimaldi castle.