In English, if you are spending time in someone’s presence, we don’t ‘make them company’, we ‘keep them company’. This is a phrase often used if someone is lonely, or is in hospital, and you might say, „I’ll come and keep you company for a while.“
The verb „to accompany“ has a slightly different meaning. Instead of simply sitting with someone, it means to go somewhere with someone so they are not on their own. So for example, you might accompany someone to the cinema, or to a ball.
A: My husband is accompanying me to the theatre on Saturday night.
B: You’re lucky, my husband is away all weekend and I have to stay at home with my baby.
A: Poor you. On Sunday, I’ll come round and keep you company.