Not being of marriageable age is a diriment impediment,

A condition, circumstance, or situation that makes an action [of marrying] null and void in its intended effects. Thus an existing marital bond nullifies any attempt to enter a second marriage.

The Church has the authority to determine impediments to marriage (cf. Session 24 on Matrimony of the Council of Trent, can. 4), but, according to the commentary of canonist Charles Augustine, O.S.B., D.D., on 1917 can. 1067,

The Code [of Canon Law] does not determine which of these [impediments] belong to the order of the natural and divine law, and which to the order of ecclesiastical law.

However,

pastors of souls should deter from it [i.e., from marriage] young people who have not reached the age at which, according to the custom of the country, marriage is usually contracted.

In this formulation the impediment is of merely ecclesiastical law, which now demands a higher age than was formerly required. The Decretals [an early codification of ecclesiastical law] followed the Roman law in reckoning the age. There was a controversy between the Cassians and the Proculejans, until Justinian adopted the view of Proculejus, who maintained that the number of years, fourteen for boys and twelve for girls, should be decisive in admitting one to marriage. The Cassians, on the other hand, held that not only age but natural capacity for the marital act should be taken into consideration. […] There are pontifical constitutions which forbid marriage to be contracted at the age of six or seven, but they do not state a precise limit.

Not being of marriageable age is a diriment impediment,

A condition, circumstance, or situation that makes an action [of marrying] null and void in its intended effects. Thus an existing marital bond nullifies any attempt to enter a second marriage.

The Church has the authority to determine impediments to marriage (cf. Session 24 on Matrimony of the Council of Trent, can. 4), but, according to the commentary of canonist Charles Augustine, O.S.B., D.D., on 1917 can. 1067,

The Code [of Canon Law] does not determine which of these [impediments] belong to the order of the natural and divine law, and which to the order of ecclesiastical law.

However,

pastors of souls should deter from it [i.e., from marriage] young people who have not reached the age at which, according to the custom of the country, marriage is usually contracted.

In this formulation the impediment is of merely ecclesiastical law, which now demands a higher age than was formerly required. The Decretals [an early codification of ecclesiastical law] followed the Roman law in reckoning the age. There was a controversy between the Cassians and the Proculejans, until Justinian adopted the view of Proculejus, who maintained that the number of years, fourteen for boys and twelve for girls, should be decisive in admitting one to marriage. The Cassians, on the other hand, held that not only age but natural capacity for the marital act should be taken into consideration. […] There are pontifical constitutions which forbid marriage to be contracted at the age of six or seven, but they do not state a precise limit.

Thus, your "series situated in XV century France, where a girl (princess) aged 8 married a +18 years old man (prince), through the Catholic Church" seems fictional.

(Also, the Church can give and has given dispensations regarding consanguinity and affinity.)