In this case we must first understand what tense the sentence is in. It is written in past tense. However the trick about this sentence is that the verb needed to be used is "faire" because in french it is said that "I did the shopping" rather than I went. The past tense of faire is fait where the personal pronoun is "I" so it is "j'ai fait" in passe compose form. So your sentence should form "J'ai fait le shopping"