Jermaine McGlashan fired the Robins into a fourth minute lead from an acute angle when he capitalised on a mix up in the Hartlepool defence.
Despite the visitors pushing hard for an equaliser in the it was Cheltenham who stretched their lead in the 37th minute.
On-loan midfielder Kemar Roofe, make his full home debut since joining from West Brom, sent a looping header over Scott Flinders from David Noble's cross.
The visitors pulled a goal back in the 53rd minute, when Franks latched on to a long clearance from his keeper Scott Flinders to slide the ball beyond Scott Brown in the Cheltenham goal.
Franks grabbed his second of the match to level the scores for Hartlepool, who have not won on the road since October 12, in the 71st minute when he fired in a shot from the 18-yard box that Brown almost kept out.