Is there a frame story structure in Hard Times?
There is no frame story structure in Hard Times -- the book is a fairly straightforward third-person omniscient narrative, with the characters described and moving the plot forward instead of flashing back or forth.
The scene was a plain, bare, monotonous vault of a school-room, and the speaker's square forefinger emphasized his observations by underscoring every sentence with a line on the schoolmaster's sleeve.
(Dickens, Hard Times, eNotes eText)
The third-person, past-tense narrative style is seen here, as there is no "I" speaking.
For a frame story structure, there would need to be some surrounding narrative to the main narrative, perhaps someone telling the story to a person or group, or a diary looking back on past events. There is a final chapter which goes over the fates of the characters, but since there is no bookending introduction or similar chapter at the beginning of the book, this is at best a coda, not a "framing" device. A good example of a frame device is Conrad's Heart of Darkness, where the story is told to the narrator by another person.