Mom is 90, and is legally blind so I do her shopping. I have sensitive skin and have always found Aveeno products to be safe, so I didn't even do my usual "sniff test" before purchasing, She told me it burned on her skin and she had to wash it off immediately: and it had a very strong fragrance. Her skin is sensitive but she hasn't had as much trouble as I do finding something that works. However, she does also have respiratory allergies and this stuff is strong enough to really bother. It's not what I'd call a light scent.
So although your new sensitive skin products may be as gentle to sensitive skin as fragrance free (yes, I realize this one doesn't say it's for sensitive skin) -- the reaction of your skin may not be the only reason for someone to want fragrance free products. I wish you'd bring yours back. I like them.
No, I would not recommend this product