Does Family Sharing allow others to see the free Apps that you've downloaded?
Yes, but not without looking.

More specifically to your iPhone scenario, to see what has been downloaded by a family member, you would need to follow the steps outlined below.

App Store


Go into the App Store app
tap on Updates at bottom right
tap on Purchased at top of screen
a list of family members will appear
tap on the family member to view their purchases


Note that by purchases we mean all downloads, as free apps are effectively treated as though they were purchased for $0.00.

iTunes

A similar process is required to view their music, movie and other iTunes purchases:


Go into the iTunes app
Tap on the More icon at bottom right
Tap on Purchased
a list of family members will appear
tap on the family member to view their purchases


Once again, by purchases we mean all downloads.

iBooks

And, with iBooks:


Go into the iBooks app
Tap on the Purchased icon at bottom right
a list of family members will appear
tap on the family member to view their purchases


Once again, by purchases we mean all downloads.