Gold In European Banks

Gold coins and bullion can be stored for safe keeping at a bank by both customers and non customers of the bank. As I understand it, such coins or bullion need not necessarily have been the subject of a physical payment transfer.

Government institutions, with international physical transfer, are just as free to make these sorts of decisions as individuals or companies.

Sorry for the rather nebulous answer, but
I suspect that there may be lots of Double Eagles still within the vaults of European banks.

I lived and worked in France for part of the 1970s and 1980s, and many banks at that time had a bullion counter with various coins on display that could be bought at the current 'cours' (a set rate of exchange that is adjusted daily) - they usually included French 20-franc pieces, British sovereigns and US double-eagles.

I've certainly seen a lot of double-eagles in France: most coin shops seem to have a pile of them, and quite a few French people have one tucked away. I imagine most of these coins would originally have been brought over by tourists doing the Grand Tour or possibly by troops during WW1. The French franc was notoriously unstable from 1914 until it was revalued in 1960, and many people hoarded gold and silver coins, and changed their savings for gold coins rather than deposit money in a bank account.

I imagine there might be some scarce and rare double-eagles lying around in French homes, whose owners think they are only worth bullion value. In 2017 I had a look through about 20 double-eagles that a Bureau de Change in Lyon was selling at the official 'cours', but they were all common dates and mints and most were in VF to EF and quite heavily bagmarked as if they'd spent most of their life being carried around in sacks, knocking against the other coins. I didn't buy any, but I have in the past bought a few gold sovereigns in France for rather less than I would have paid in a local coin shop.

I would think it would be impossible to buy a Double Eagle anywhere in the World today, for gold value plus a percentage; they are all sold as a numismatic item and as the RedBook suggests, at a fixed price according to condition and market condition pricing, as with all other numismatic 'bullion' items.

You have done well!