I received an email saying that we have a subscription to Apple TV through July. When I try to access the subscription via my laptop, the only option is to sign up for Paramount which provides only one month free.

Apple TV+ (note the Plus) and Paramount+ are independent content providers with independent subscriptions.

If you select a “featured” (promoted) show from Paramount+ to see, then you may be re-directed to subscribe to that service first.

• With an Apple TV+ subscription you get access to all of the Apple TV+ content, not Paramount+ content.
• With a Paramount+ subscription you get access to Paramount+ content. Subscribing to Paramount+ in the Apple TV app starts with a free week trial (not a month). Subscribing to Paramount+ in the Apple TV app would then require you to watch this subscription content in the Apple TV app. Paramount+ allows Channel subscribers to create an additional Paramount+ account for viewing in their dedicated app (iOS/iPadOS/tvOS), or on the web, or on third party devices.

Also see your current subscriptions overview.

Apple TV Channels FAQ: Services, pricing, availability, and everything else you need to know - Macworld

Subscribe to Apple TV channels in the Apple TV app - Apple Support