While there is nothing in their answer which is wrong, and it is a fantastic answer on the 'Pale of Calais' as a whole, I think u/ixnay2000 may be overstating the degree to which Calais itself was Dutch or French speaking during English rule, especially at the beginning. After Edward III conquered Calais in 1347 he expelled its citizens and settled it with English merchants and soldiers. During the following decades he offered grants for anyone wanting to move to Calais and restricted locals from moving back, aiming to establish Calais as a loyal English city capable of supplying military campaigns and chevauchées, and also limit the city to the defensible part of the Pale. This resulted in Calais becoming almost entirely English speaking, although a relatively small city of only 2000. After the Treaty of Brétigny in 1360 the Pale of Calais became an integral part of England, as opposed to other English possessions in France, later sending representatives to Parliament. Most importantly though for the future of Calais' demography, was that in 1362 it became a 'staple port' - a port with a monopoly for importing certain goods from mainland England.

However, for various reasons to do with the methods of tax collection used by England in this period, which are probably slightly too complicated and long-winded to go into in this question, export duty on wool was an incredibly important source of income for the English Crown, making up more than 80% of their revenue in some years. This meant that as Calais's importance as a staple port grew, its importance to the English treasury also grew, and it became more vital for Calais to keep expanding and increase contributions to customs fees than it was for it to remain impregnable. In order to ensure that Calais could handle this amount of trade, the restrictions on locals moving back to Calais were lifted (or more accurately 'forgotten') and over the next fifty years its population grew to around 12000, the majority of whom were now locals. That's not to say though that there wasn't a considerable amount of English people still in Calais, of all classes, for whom English would have been their native language. This core of English citizens remained for the entire Hundred Years War, but I cannot speak of the degree to which it continued into Tudor times.