We know that children from noble families had little say about with whom they were going to marry, was that the same for commoners, or they had more freedom at the time of marriage?

Depended on how propertied the family was. Peasants as well as nobility tried to improve the productivity of their land through strategic marriages. It was somewhat less common, in part because landholding tended to be less continguous so it wasn’t always possible to make that kind of advantageous marriage.

But the less property there is to inherit, the less that matters. Not that families wouldn’t be concerned about making sure that their kids made “appropriate” matches that would ensure the economic viability of the new household, but there was more flexibility.