I doubt the French cared much one way or the other. In his short life Napoleon II wasn't much involved with France, being King of Rome, then Prince of Parma and finally, after his dad's abdication, Duke of Reichstadt. For most of his adult life until his death he lived in Austria with his maternal grandfather's family.
But an equally curious bit of trivia is that his heart, which as you say was put in a jar and kept in Austria ... still sits in a special vault, the Herzgruft (Hearts Crypt), along with the potted hearts and bottled other bits of another 53 members of the Habsburg family. Napoleon II's heart is in urn 42 and his intestines in urn 76.
..... Which would comprise a veritable Smörgåsbord for that eccentric epicurean dean Dr William Buckland ... ("Talk of strange relics led to mention of the heart of a French King [Louis XIV] preserved at Nuneham in a silver casket. Dr. Buckland, whilst looking at it, exclaimed, 'I have eaten many strange things, but have never eaten the heart of a king before', and, before anyone could hinder him, he had gobbled it up, and the precious relic was lost for ever." Augustus Hare, The Story of My Life, vol. 5, p. 358).