You need to remind people of the facts in this part of history.
1) Charles was appointed Constable of France and given Governorship of Milan, by Francis I of France in 1515.
2) Francis I, has claimed the throne through his marriage to Claude, Duchess of Brittany, daughter of Louis XII and because he is the Great-Great grandson of Charles V of France, through Charles's son Louis I, Duke of Orleans
3) Renee is also the daughter of Louis XII.
4) This leads to Constable being slightly linked to the throne.
5) Francis was uneasy with the proud and wealthy duke, and soon recalled him from Milan and refused to honor his debts. Charles was further angered by the appointment of Charles IV of Alençon, the King's brother-in-law, as commander of the vanguard during the campaigns in the Netherlands, an office which should have been his.
6) The death of his wife in 1521 provoked the final breach between Charles and Francis I. Suzanne had left all her estates to Charles, but the King's mother, Louise of Savoy, claimed them as the heir in proximity in blood, due to their previous entailments. She proposed to settle the question by marrying Charles; he refused the proposal because Louise was over forty-five years of age and fourteen years older than him. On behalf of his mother, Francis confiscated a portion of the Bourbon estates before the lawsuit had even been opened. Seeing no hope of prevailing, Charles made a secret agreement to betray his King and offer his services to the Holy Roman Emperor Charles V. The Emperor, the Constable, and King Henry VIII of England devised a grand plan to partition France. This however came to nothing because the plot was discovered; Charles was stripped of his offices and proclaimed a traitor. He fled into Italy in 1523.
So before a marriage between Charles III, Duke of Bourbon and Renee of France can be possible, we need two items cleared up.
1) Charles IV, Duke of Alençon, died in 1525 aged 36, if he was to die in 1521 aged 32, King Francis would appoint Charles as commander of the vanguard during the campaigns in the Netherlands, making Charles think this is why he was called back from Milan.
2) Louise of Savoy, died on 22 September 1531, aged 55, if we could kill her off in 1521 aged 45, this would mean that she would not make her son, King Francis I, support her claim.
With these two issues crossed, it could be possible for Charles to at least ask for Renee's hand, although, Francis might suggest that Charles marries his sister, Marguerite of Angoulême (Louise of Savoy's daughter)