Bonjour Joakim,

In French, you will use the same verb to express "to be bored" and "to get bored": s'ennuyer.

In the past tense you will be using either L'Imparfait or Le Passé Composé, to express slightly different nuances, as follows:
- Je me suis ennuyé  means "I was/got bored" at the time, but this action/state is finished, over now.

- Je m'ennuyais expresses more a state in progress, like "I was being/getting bored", or a habit, a repetitive action like "I used to be bored".

I hope that's helpful.