You don't need the comma... He noticed that under a big tree there was a big basket. I believe that is grammatically correct; nevertheless, it would sound a lot better if you said 'He noticed that there was a big basket under the tree.' I would also try and vary the sentence a bit more.... So instead of saying 'big tree' and 'big basket' you could say 'enormous basket!' or 'huge tree.' I hope that helps : )

No. He noticed a big tree. Under the tree was a big basket.