My gut says the concern arose around the balance of gold, which would behave differently. But that really doesn't work with Bastiat's example, because there is no flow of gold (or other currency) in or out of either country.

But the fact that there is no flow of currency makes the problem look stupider. England is notionally benefiting because it has gained some wine "worth" 50 francs while losing some coal "worth" 70 francs. France is suffering because it's lost some wine worth 50 francs while gaining some coal worth 70 francs. With no francs traveling abroad, the matter is closed and France has ended up better off. What was the problem?

From this perspective, "trade deficit" appears to be synonymous with "gains from trade". (But note that the analogy falls apart immediately; England is also experiencing gains from trade, but it has a surplus instead of a deficit. The difference is driven by the artificial division of the trade into two legs, one of which happens first. If the import happens first, you get a surplus. If not, you get a deficit.)

With fiat, I think there is a concern floating around that if some foreign party absorbs a lot of our currency, and then we print more to replace the loss (so that we continue to have an appropriate amount domestically), the foreign party could suddenly crash the value of the currency by deciding to spend it. That's true. It can't be the origin of the fear of trade deficits, though, because nothing similar appears in Bastiat's example, where currency never moves. It's more analogous to the traditional fear of seeing your country's supply of gold drained away by trade.