Thank goodness it's not just me - I heard the exact same thing! Even after I had slowed it down and discerned the separate 'La', I still had to put 'vance' in the absence of anything that sounded even remotely different. I played the correct solution over and over again and I would be here until voomsday before I heard what it is supposed to be. This is far from the first time I've had this problem on DL.
It really sounds just fine to me. Besides the more obvious differences in vowel pronunciation, French is somewhat different in how it makes these consonant sounds, too. The d is not as sharply distinct as it is in English, just a bit softer, with less push from the breath. I find, when I try to reproduce it, that I put the tip of my tongue a bit further back - not just behind the teeth, but touching the alveolar ridge instead.
And yet a little further on in the exercise there was another example of 'La danse' that sounded perfectly fine to me too. As I say, it's not the first time I've come across these acoustic anomalies in DL. The very next time I come across that version of 'Les' with a very definite 'p' in front of it, I'll flag that one up as well. And I can't be the only one who gets the word 'singe' with the sound like the speaker fell off her chair as she was saying it!
The expectation is that you will hear what is being said and that is the sense of the instruction. If you just write whatever you think you hear, don't expect it to be accepted if it is not what the speaker says. Especially in the early stages of learning, sounds may not be easily discerned. That will improve with practice. Hang in there.