There is no firm evidence that Louis XIII was gay or bisexual, but there is some anecdotal evidence he was gay.
We also need to remember that the sexual mores of the 1600's were very different from today. Men and woman, at times and places, were more demonstrative with friendships of the same sex than they are today.
On the other hand, the intense emotional ties that Louis developed with a series of handsome men clearly indicate his homosexual tendencies. However, there is no evidence (apart from unreliable anecdotes) that he ever engaged in homosexual acts with these favorites.
The first of these men was Charles d'Albert de Luynes (1578-1621), who entered the young king's service in 1611 and rapidly became the boy's closest friend and adviser, despite the 23-year age difference. Luynes helped engineer the assassination of Concino Concini (1575-1617), Marie de Médicis's favorite, on April 24, 1617, thereby putting an end to the queen mother's authority (she governed France as Regent until 1614, then as head of the Royal Council) and instituting the king's personal rule.
Louis was particularly ill at ease with women. He married a Spanish princess, Anne of Austria, on November 28, 1615, but their wedding night was a disaster, and the marriage remained unconsummated until 1619. He thereafter occasionally managed to sleep with the queen, but only from a sense of duty.