Joan of Arc was captured at Margny-lès-Compiègne the 23th May 1430. A Burgundian archer who accompanied the Bastard of Wandonne pulled her from her horse. By decree of the duke of Burgundy who met her the same night, Joan of Arc was delivered to his leading commanding officer in Picardy, John of Luxemburg, lord of Beaurevoir.
Philip the Good, duke of Burgundy, sent letters to all his allies that his army had captured the Pucelle. Two or three days later already, by the 25th or the 26th of May, Martin Billorin requested the duke for Joan to be delivered to the Church, so that she may be tried for heresy. Martin Billorin was a master theologian and vicar to Jean Graverevent, who was the inquisitor of faith for the kingdom of France.
A second letter was sent to the duke of Burgundy by the University of Paris, which held the most prestigious faculty of theology in christendom at the time. The theologians of Paris also demanded for Joan of Arc to be tried by the Church. They even sent another letter to the same effect, dated to the 14th July 1430, to John of Luxemburg.
John of Luxemburg had to play it smart. A little prior to Joan's capture, Henry VI of England, whose partisans claimed to be the king of both England and France (and John of Luxemburg was one of them), set foot in France in April--and it was no funny business.
The wealthy cardinal of Winchester, Henry Beaufort, who effectively ruled England whilst Henry VI's minority--to the great disgust of the duke of Gloucester--secured the funds for the young king of England to cross the channel and be coronated in Paris, at Notre-Dame. It was a symbolic, religious and political answer to Charles VII's coronation at Rheims, that was held in July 1429.
Winchester had been in the middle of heavy preparations for the launch of a new crusade when he dropped everything to rescue his cousin/nephew/I-can't-remember-and-it-doesn't-really-matter, the duke of Bedford, who ruled France for Henry VI. Winchester started to raise funds as early as in September 1429, and by February 1430, the expedition was more than secured.
In all a force of some 5,000 men was to be shipped to France, and this was in addition to the 2,259 men who had already been sent as reinforcements under the Bastard of Clarence at the beginning of the year at a cost of £11,600. The wages alone for the royal expedition amounted to some £35,000 for six months. (G. L. HARRISS, Cardinal Beaufort. A Study of Lancastrian Ascendancy and Decline. Oxford: Clarendon Press, 1988. p. 194)
A lot of money, a lot of men and the king of England and France himself had just arrived in France from accross the Channel, only a few days before Joan was taken.
However the Church, the faculty of theology of Paris especially, directly demanded for Joan of Arc to be tried for heresy. Moreover, though she was a prized captive due to her public role in the latest developement of the Hundred Years' War, she had no real money of her own.
At first, she was kept at Beaurevoir, deep in Burgundian territory. The area was surrounded by castles directy controled by John of Luxembourg. Any commando attempt to rescue her while he was lording over his own castles and lands would have resulted in a disaster. He locked Joan up in a tower, yet she tried to escape and jumped from the top of it. She survived the fall. John of Luxembourg caught her back as she didn't go very far and locked her up for good this time.
Meanwhile, a man who had crossed the Channel along with Henry VI had a good reasons to seek revenge from Joan of Arc. That man was was Pierre Cauchon, bishop of Beauvais, who had recently lost control of said town of Beauvais in August 1429, following the events of Orléans and Charles VII's coronation at Rheims. A man loyal to the latter had recently been dispatched to command that heavily fortified city, Étienne de Vignoles, aka "La Hire", as bailli of Vermandois--we'll talk about him a bit later.
Following the example of Martin Billorin and the theologians of Paris, Cauchon, who'd gone in exile for a bit less than a year and now aspired to become the archbishop of Rouen, requested Joan too. He had better arguments on the matter than those who called to the duke or Burgundy and John of Luxemburg before, for he was still at the time the bishop of Beauvais. Joan had been captured in his diocese. She basically fell under his spiritual jurisdiction. Along with the promise of a grand compensation, he managed to convince Philip the Good and John of Luxemburg to deliver Joan to him so that she could be tried at Rouen. Winchester himself advanced the money to speed up the process.
Come November 1430, Joan of Arc was eventually transfered from Beaurevoir and sent on her way to Rouen, where she arrived two days before Christmas, on the 23rd December.