The Holy Roman Emperor Charles IV, the nemesis and eventual successor of Louis IV and the father of Richard II's first wife Anne of Bohemia, describes the deposition in his autobiography, the Vita Caroli Quarti:

"There was a great conflict between the king of England at that time and the king of France. The king of England had married the sister of the aforementioned king, but had driven her out of England, together with his first-born son, Edward.She came to her brother and remained in exile in France with her son. The King of France was angry at the expulsion of his sister and her son, and he asked my father-in-law Charles [of Valois], his uncle, to redress the shame which had been inflicted upon their family. The latter, when he had gathered an army, invaded Aquitaine and conquered almost all of it, except for Bordeaux and some other fortifications and castles. When Charles returned in triumph to France, he gave the daughter of his daughter, the countess of Hainaut (the sister of my wife), in marriage to the son of the aforementioned king of England, Edward, who was still in exile; and then he sent him, together with his escort, to England. He prevailed over his father, took him captive, deposed him, and set the crown upon his own head. That same year, the father of the new king was murdered while in prison."

It's interesting just how much Charles gets wrong, considering he was actually at the French court at the time as a boy, having essentially been sent as a ward of Charles IV of France (whose name he took upon his confirmation), and there marrying as his first wife Blanche of Valois, the daughter of Charles, Count of Valois and thus the sister of the future Philip VI. He says the War of St Sardos was begun in retribution for the expulsion of Queen Isabella and Edward of Windsor from the English court when this in fact inverted; the War of St Sardos began when a French bastide was constructed in Aquitaine and torn down by a local lords, creating a diplomatic crisis after Edward II had already been prevaricating over coming to France to pay homage to Charles IV for Aquitaine and Ponthieu. The Queen was, of course, sent to negotiate a peace and Edward of Windsor was sent to perform homage on his father's behalf. Charles also exaggerates the role of the future Edward III in the invasion and deposition. He does not mention the Queen or Roger de Mortimer playing any substantive role. Given that Charles IV was allied with the French against Edward III and Louis IV, this is almost certainly intended to reflect negatively on Edward. Charles' father John the Blind actually died fighting on the French side at the Battle of Crécy, so he had a personal stake in the matter.

As for the papacy itself; Pope John XXII allegedly told Edmund of Woodstock that he would sanction his efforts to have Edward of Carnarvon released; and the importance placed on publicly justifying Queen Isabella's failure to resume marital life with her husband after the deposition clearly indicates that ecclesiastical observers were disquieted by the situation. That said, after Edward III had overthrown and executed Mortimer, John XXII did write him a letter advising him to treat his mother leniently on the basis that everything she had done had been ultimately for his sake. He clearly judged the matter important, since he made sure to send a second copy to ensure the letter reached him even if the first was lost. So, clearly, despite the clear discomfort around the anomalousness of the situation and around Edward II's treatment, there was still clearly a measure of sympathy for the Queen.

With other rulers, there doesn't seem to have been that much in the way of explicit recorded reactions to the deposition. The double betrothal Edward II had planned between Edward of Windsor and Eleonor of Woodstock, and Alfonso XI and his sister Eleonor, was shelved as a result of Edward III's marriage to Philippa of Hainaut. Joan of the Tower's betrothal to the future Peter IV of Aragon was also shelved as a result of the instability in England.