Question: Who is the paternal grandfather of Joan I, Countess Of Burgundy?

Isabella of Bourbon
Isabella of Bourbon, Countess of Charolais( 1434 – 25 September 1465) was the second wife of Charles the Bold, Count of Charolais and future Duke of Burgundy.
She was a daughter of Charles I, Duke of Bourbon and Agnes of Burgundy, and the mother of Mary of Burgundy, heiress of Burgundy.
Joan I, Countess of Burgundy
Joan I (1191–1205), also called Joanna of Hohenstaufen, was ruling Countess of Burgundy 1200-1205, daughter of Otto I, Count of Burgundy, and Margaret, Countess of Blois.
Born in 1191, Joan was countess from the time of her father's assassination at Besançon in 1200 until her own death in 1205, whereupon her sister, Beatrice II, succeeded her.
Joan III, Countess of Burgundy
Joan III of Burgundy( 1/2 May 1308 – 10/15 August 1347), also known as Joan of France was a reigning Countess of Burgundy and Artois in 1330 – 1349, She was also Duchess of Burgundy by marriage to Odo IV, Duke of Burgundy.
She was the eldest daughter of King Philip V of France and Countess Joan II of Burgundy.
Florine of Burgundy
Florine of Burgundy( 1083–1097) was a French crusader.
She was the daughter of Eudes I, Duke of Burgundy and Sybilla of Burgundy.
Her maternal grandfather was William I, Count of Burgundy.
Florine was married to Sweyn the Crusader, a son of Sweyn II of Denmark.
Joan II, Countess of Burgundy
Joan II, Countess of Burgundy( 15 January 1292 – 21 January 1330), was Queen of France by marriage to Philip V of France, and ruling Countess of Burgundy and Countess of Artois.
She was the eldest daughter and heiress of Otto IV, Count of Burgundy, and Mahaut, Countess of Artois.
Matilda II, Countess of Nevers
Matilda II, Countess of Nevers( 1234/35–1262), also known as Maud of Dampierre or Mathilda II of Bourbon, was a sovereign Countess of Nevers, Countess of Auxerre, Countess of Tonnerre and Lady of Bourbon.
She was a daughter of Archambaud IX of Bourbon and Yolande de Châtillon, Countess of Nevers.
As heiress to the counties of Nevers, Auxerre and Tonnerre, she was married off to Odo, Count of Nevers, the son and heir of Hugh IV, Duke of Burgundy.
By this marriage Odo reunited two important areas that had previously been united as the Duchy of Burgundy, but he died leaving no male heirs, and so the united territory passed to his brother Robert II, Duke of Burgundy.
After her father's death Matilda also became Lady of Bourbon.
With Odo she had three children:
Blanche of Burgundy, Countess of Savoy
Bianca of Burgundy( 1288 – July 1348), was a Countess consort of Savoy, daughter of Robert II, Duke of Burgundy, and Agnes of France.
She married in 1307 Edward, Count of Savoy.
She was mother of Joan of Savoy.
In 1346 and 1347, she was an influence at the court of her nephew, Amadeus VI to pursue closer alliances with Burgundy to offset the pending sale of the Dauphiné to France.
This led to his brief engagement with Joan of Burgundy, daughter of Philip of Burgundy and Joan I, Countess of Auvergne.
She died July 1348, perhaps from the Black Death.
Sibylla of Burgundy, Duchess of Burgundy
Sybilla of Burgundy( 1065 – 1103), was a French noble, Duchess consort of Burgundy by marriage to Eudes I, Duke of Burgundy.
She was a daughter of William I, Count of Burgundy and Stephanie.
She was married to Eudes I, Duke of Burgundy in 1080.
Children:
Otto I, Count of Burgundy
Otto I (between 1167 and 1171 – 13 January 1200) was Count of Burgundy from 1190 to his death and briefly Count of Luxembourg from 1196 to 1197.
He was the fourth son of Frederick I, Holy Roman Emperor, by his second wife Beatrice I, Countess of Burgundy, daughter of Count Renaud III.
Philip I, Count of Auvergne
Philip of Burgundy (November 10, 1323 – August 10, 1346) was Count of Auvergne and Boulogne (as Philip I) in right of his wife and was the only son and heir of Odo IV, Duke of Burgundy, and of Joan III, Countess of Burgundy.
His mother was the daughter of King Philip V of France and of Joan II, Countess of Burgundy.
He married Joan I, Countess of Auvergne and Boulogne, in c. 1338.
In 1340, he fought with his father who defended the city of Saint-Omer against the assaults of Robert III of Artois.
In 1346, he participated in the siege of Aiguillon, led by John, Duke of Normandy (the future John II of France).
It was during this siege that he died, after falling from his horse.
His widow Joan remarried in 1349, her second husband being King John II of France.
Since Philip had no other sons from his marriage to Joan, the future of the House of Burgundy was then placed in the hands of his young son Philip (1346–61), who died childless.
After the death of the younger Philip, the dukedom of Burgundy became a part of the French crown, and was granted by John II of France to his youngest son (and the previous Duke’s stepbrother), Philip the Bold.
His daughter, Joan (134411 September 1360), was betrothed to Amadeus VI, Count of Savoy from 1347 to 1355, and was raised at his court.
When she was released from the engagement at age 10, she entered a convent at Poissy, where she remained for her final years.

Answer: Frederick I