Okay, here's the Wikipedia article:

The Commune named François Jourde [fr; it; oc; ru] as the head of the Commission of Finance. A former clerk of a notary, accountant in a bank and employee of the city's bridges and roads department, Jourde maintained the Commune's accounts with prudence. Paris's tax receipts amounted to 20 million francs, with another six million seized at the Hôtel de Ville. The expenses of the Commune were 42 million, the largest part going to pay the daily salary of the National Guard. Jourde first obtained a loan from the Rothschild Bank, then paid the bills from the city account, which was soon exhausted.

The gold reserves of the Bank of France had been moved out of Paris for safety in August 1870, in addition to 88 million francs in gold coins and 166 million francs in banknotes. When the Thiers government left Paris in March, they did not have the time or the reliable soldiers to take the money with them. The reserves were guarded by 500 national guardsmen who were themselves Bank of France employees. Some Communards wanted to appropriate the bank's reserves to fund social projects, but Jourde resisted, explaining that without the gold reserves the currency would collapse and all the money of the Commune would be worthless. The Commune appointed Charles Beslay as the Commissioner of the Bank of France, and he arranged for the Bank to loan the Commune 400,000 francs a day. This was approved by Thiers, who felt that to negotiate a future peace treaty the Germans were demanding war reparations of five billion francs; the gold reserves would be needed to keep the franc stable and pay the indemnity. Jourde's actions were later condemned by Karl Marx and other Marxists, who felt the Commune should have confiscated the bank's reserves.[57]

The only source cited in this subsection is Marx.

The financial measures of the Commune, remarkable for their sagacity and moderation, could only be such as were compatible with the state of a besieged town. Considering the colossal robberies committed upon the city of Paris by the great financial companies and contractors, under the protection of Haussmann, the commune would have had an incomparably better title to confiscate their property than Louis Napoleon had against the Orleans family. The Hohenzollern and the English oligarchs, who both have derived a good deal of their estates from Church plunder, were, of course, greatly shocked at the Commune clearing but 8000 f. out of secularization.

So no evidence of anarchist concerns dominating the maintenance of the Bank of France so far. Let's dig a bit deeper: from page 56 of Massacre: The Life and Death of the Paris Commune of 1871 by Merriman (2014), as recommended by the Wikipedia authors:

The Commune named François Jourde as delegate for Finance. On 19 March Jourde and Eugène Varlin went to the Bank of France to ask politely for a loan of 700,000 francs. This they received. The Commune also received a credit of well over 16 million francs – though it was a paltry sum compared with the 258 million francs credit Versailles received from the Bank of France, making possible the reconstitution of the French army. The Rothschild banking family also loaned money to the Commune. The Commune remained attached to legalism and did not confiscate funds in the Bank of France, which it easily could have done, but it did begin to mint its own coins in mid April.

Now we're getting somewhere. Varlin was a Proudhon enjoyer, and Proudhon was a market enjoyer. Frankly, there are definitely Proudhon enjoyers in the modern anarchist movement (mutualists), but most anarchists these days would consider Proudhon a reformist and disagree with a lot of his ideas on economics...and frankly, this is a perfect example of why I disagree with mutualists about market economics. So certainly an anarchist refused to seize the Bank of France.

Which, I 1000% agree with Marx in his later writings on this (but from an anarcho-communist perspective) that this was an error in judgement on the Communards' part, e.g. in Marx to Domela-Nieuwenhuis, 22 Feb. 1881 (Karl Marx Selected Writings page 642, same reference as Wikipedia): "The appropriation of the Bank of France alone would have been enough to put an end with terror to the vaunt of the Versailles people, etc., etc...."

But unless someone has a source that goes into more detail than that, which by the way is why I asked the person I replied to instead of searching for it myself, we don't have enough evidence on hand to conclude that the anarchists (or even the Proudhonist faction as a whole) collectively were responsible for this error in judgement.

All the books I referenced are available on LibGen 🏴‍☠️. Also anyone who replies to this, feel free to tag my SDF account because SDF is taking a dive for a few hours.