Different companies will have different operating procedures, however all will stop if a fire warning sounds prior to V1.
In the company that I work for, operating Boeings, we split the actions into 3 segments -
1 - reject the take off to a full stop.
2 - identify and deal with the reason for rejecting, some events have "recall items" that are completed from memory.
3 - if needed order an evacuation.
In our company, only the Captain can decide to stop, the FO will alert the Captain to the fault.