Eu faço as compras - Je fais des courses - I shop I go shopping isn't very natural in English, because they don't have this tense the "future proche" as we do in French and in Portuguese. So you can say Je vais acheter in French ou Eu vou comprar in Portuguese, but not I go shopping in English. They say "I'm going shopping", instead.

ir em mercearia = go grocery shopping ir fazer compras = go shopping

I go shopping