If my partner and I were never married and never did any legal act to certify our union, could I have access to his pension in the event of my death?

Yes, you can prove that you are living together as a common-law couple (UMH) using all the means of proof available to you. For example, through extrajudicial statements from third parties who are witnesses to your relationship, photos, your affiliation as a beneficiary of health services, the fact that you have had children together, among others.