If it was a lower purity, then when they sold the 129 tons, they would not have obtained 129 tons of "higher purity" gold and still turned a profit. They would have gotten fewer tons of gold. Your logic has the wrong sign.

Also, the fact that gold prices are rising means when France sold the gold and then purchased it later, the higher price to obtain the same quantity of gold would mean they incurred a loss, not a profit. Here, too, your sign is wrong.

Finally, at current prices, 129 tons of gold is worth $19 Billion dollars in total. It seems hard to believe that short term price declines (which is what is needed to turn a profit) would be such that gold fell over 80% in value, which is what would be needed to sell 129 tons of gold, then wait a while and buy 129 tons of gold, and end up with a profit equal to over 80% of the price of gold in question.

Moreover, rising gold prices would cause the French to earn a loss, not a profit

Seems counterintuitive to me. This would only make gains when they bought the new gold before selling the old, or when there's some arbitrage going on between Gold/USD, Gold/EUR and USD/EUR.

If they first sold the old for USD, then bought the new for USD, with a rising gold price, they'd miss the price-gain during the time between the trades, when they held the USD. It'd be a loss, not a gain.

If there's some arbitrage going on, then I highly doubt that brings $15B gain. The differences would have to be huge.

I think the (author (AI)) writing that article is simply mixing up stuff. I think this gain is not a cause-effect of the conversion, merely the gains from rising gold prices on the gold it holds over that period.