To make things straight, before we move to the historical aspects of the issue, I'll allow myself to glance upon the status of veracity in fiction and the author's background that could have influenced this particular way of thinking. First and foremost, the idea of aging does not really apply here as the tale referred to in Chesterton's story is told by doubly unreliable narrator, as it is referred by a character conveying a tale heard previously from someone else, while Father Brown himself is also not a scholar and, even though well-educated, he can simply be wrong.

On the other hand, the persona of Father Brown is sometimes used by Chesterton as a stand-in for his own opinions on various subjects and thus might be, to at least some extent, biased. I assume that the author of the question is aware of this, but for the sake of people less acquainted with Chesterton and his works, I'd like to mention that he was a Catholic convert and devoted substantial part of his non-fictional work to Catholic philosophy, meaning that this topic was undoubtedly important to him. The referenced passage is the more important, as one of the facets of said philosophy creator of Father Brown focused extensively was the Catholic Social Teaching, largely developed in the wake of the publication of the Rerum novarum Encyclical by the Pope Leo XIII in 1891 and the ideas of a medieval social justice presented by Father Brown in the story are very much in line with the social doctrine of the Catholic Church in early 20th century. The topic was the more important to Chesterton that he, in cooperation with his close friend Hilaire Belloc (a historian, largely thought to be a main force behind Chesterton's conversion) formulated the doctrine of distributionism, opposed to both modern capitalism and socialism and based on the prevalence of local private businesses united in modern incarnation of guilds, control over the banks and large companies to prevent abuse of a financial system and creation of monopolies, and a system of welfare that would help people in need (these ideas were also adopted in USA by e.g. Catholic Worker Movement that merged ideas of Chesterton and Belloc with those of Dorothy Day and Peter Maurin). As one can see, the diatribe of Father Brown is not only a presentation of the medieval history but also a thinly-veiled criticism of early-20th century economic systems.

Now, after this somewhat long-winded prelude, lets discuss the actual veracity of the statements presented by Father Brown. We need to note, however, that the historical implications notwithstanding, the story, although not that probable, is definitely not impossible, given that a lot of people in history broke the laws and some of them could have even went unscathed. Everything in the story could have happened, probably to the horror and disgust of the local people, but it could have happened, especially if there was more to the story that has been told by the characters.

The principle rendered by Father Brown as salvo managio suo ('except one's own sustenance') or the ruling forbidding the seizure of the tools of the trade belonging to the debtor is not a concept limited to Middle Ages, as it was largely present in legislation when Chesterton was writing The Curse of the Golden Cross and is still used. Provisions both medieval and modern prevented seizure of essentials, such as food, tools, beds, everyday clothes, educational and religious books or last farm animals were common in British and American laws, while even the least debtor-friendly regulations exempted at least the tools from seizure. This, of course, does not mean that creditors did not try to seize such items, usually resulting in police interventions and trials, as attested by court ledgers from the times as late as early 1930s.

The problem with the story presented to Father Brown and a good indication that it is a modern fabrication, is the fact that in Middle Ages, or, specifically, in 13th century, Jewish creditor would be able to seize anything. If the debtor was unable to pay the loan back, Jewish usurer would have needed to bring the matter to the appropriate court. This changed in the end of 12th century with the creation of the Exchequer of the Jews (Scaccarium Judaeorum) and granting relevant royal officials the power to distrain debtors of the Jewish moneylenders, meaning that defaulting debtors were attracting direct royal scrutiny. But said debtors were usually landowners, not urban craftsmen (who could have wlways used urban financial institution of guild's support). And indeed, exploitation of the land trade associated in Jewish debts (Jews could have been taking land as a collateral, but were not able to possess the land, so they needed to sell it immediately) was one of the major causes of the Second Baron’s War in 1260s. Thus, if the buyer of the cross was another noble rather than a goldsmith, the story would have been much more plausible.

The remark that a person not having anyone to support them is not a medieval idea is largely correct. Middle Ages, especially the central part of the period that the tale was allegedly set in, was a time of a widespread self-organization that basically formed the very basis of the medieval society. With few secular institutions around, people were organizing themselves, with majority of the interactions having very personal, individual character.

If the man in question was indeed an urban craftsman, he would have likely belonged to the craft organization and would have been helped by his fellow craftsmen, as the organizations like these were created precisely to support the interests of the members, including mutual help for both members and their families. In general, it would have been relatively difficult for a single craftsman to fall on a very hard times, because that would require sudden lack of commissions or lack of remuneration for the performed work, what is highly improbable in medieval setting. Guilds were controlling relevant markets in the city and thus making sure that all members have a steady influx of commissions was part of their basic tasks. This also meant that anyone who tried to weasel out of the payment had to deal with the entire organization, most often than not supported by local urban authorities, and this was a force that even a monarch would be wary to antagonize, especially if we're speaking of a major city.

On the other hand, we can't forget that the goldsmith mentioned committed suicide, a mortal sin in the eyes of the Church, so it is possible that in despair strong enough to even consider ending his life, he might have started to blame God for his misfortune and this kind behaviour (obviously opposite to what was expected of a pious Christian, as exemplified by the biblical story of Job) could have alienated him from other people who would have treated him as a blasphemer, what includes his immediate family. Such behaviour would also result in his dismissal from the guild and cessation of any ties with former craftsmen. But this also mean that such blasphemy was known publicly, and in such case, if the goldsmith was to hang, it wouldn't be by his own hand.

Now, concerning Jews, although what Father Brown says is largely true, especially for some areas in Europe, position of Jews in Western Europe was precarious since the late 11th century, in the wake of the crusade movement and rising millenarism. This is especially true for 12th- and 13th-century England, i.e. late years of the reign of Henry II and the reign of John. Jews were usually a subject to exorbitant taxes that were sometimes nothing more than ransoms for the rich community members imprisoned for no reason other than extortion.

The position of servi regis mentioned basically mentioned that the Jews were nominally protected by the king as they were in royal employ, but the kings had virtually no obligation to keep up their end of bargain and Jews, due to their limited legal status and generally low numbers, were unable to organize any meaningful opposition. In addition, as they basically functioned outside the feudal system of legal dependencies, Jews were flocking to royal cities as the king was the only instance that could have provided them modicum of protection. Nevertheless, anti-Semitic riots and massacres, although uncommon, were definitely present, although they were often instigated by people instilling religious fervour in others, whether illicitly, such as various millennarian sect leaders or using official authority, such as Giovanni di Capestrano who orchestrated an execution of few dozen Jews in Vratislav and Svidince in Bohemia (now Wrocław and Świdnica in Poland) in 1453.