I've got one-year of access to Apple TV+ free with the purchase of a new iPhone
To accept the offer, users have to redeem it on their new Apple device in the TV app. The free subscription is not automatic. Subscribing without redeeming the offer will result in regular monthly fees.
but I am being charged every month. Since the access is free I do not have the option under "Subscriptions" to "cancel" (it shows as free).
Every subscription on your Apple ID account can be canceled, including free trials. Canceling during the trial period will expire the service immediately, and then the free period can’t be reinstated later.
How to cancel a subscription from Apple - Apple Support
If your Apple TV+ subscription is still listed as “Free for 1 year”, and with a first billing date in the future, then the charge may be for something else. See you purchase history for details. It will list all charges to your Apple ID account, including subscription fees. See your purchase history for the App Store, iTunes Store, and more - Apple Support
Contact the Apple Support staff to see if any unintended situation can be altered for you, start online, or contact them directly by phone.