I'm sorry, but this is a terrible example sentence. Who on earth would refer to walking their dog as "taking a walk with" their dog? The dog has no independence. It doesn't join you for a walk the same way your friend Julie might.
The example sentence should be changed to:
Anne et Antoine promènent leur chien.
You can have the same answer choices, but the correct answer would be "Anne and Antoine are walking their dog." Which is a sentence you might say in real life, as opposed to "They're taking a walk with their dog" which no one said ever.