To see the full conversation, go to Alizée's page. At the right side of one of her posts, click on "open". Note that the "open" doesn't show until you move your mouse over it.
This will expand the post to show the whole conversation.
I believe when you look at a person's page, you only see their tweets and retweets, unless you "open" a post to see the responses connected to it. I don't think the old version of Twitter worked the same way.