I often stay at the LeMeridien in Frankfurt, which is just opposite the main station in FRA and a 15 minute train ride to the airport.
The Sheraton FRA is usually quite expensive, so there are better deals to be obtained in Frankfurt - provided there is no trade fair at that time.
You can check your bags at the FRA airport train station and then casually walk over to the FCT. Train station to FCT is a 10 minute walk.