Okay, I talked this over with a friend of mine, so he convinced me that I ought to use Time Travel as the FTL of choice.
Why you ask?
Well, I was originally going to go with a jump drive. Works the same way as a time machine (in principle). However, since time travel is the most efficient way sentient beings can get around this universe, it only makes sense to use a time machine.
It's your choice, but... have you considered the consequences ? If time travel exists and is widespread enough that it can be used industrially (for spaceships), then it means that many people can go back in time and rewrite history. In the best-case scenario, you play a gonzo sci-fi version of Valerian or Feng Shui, with character waking up in a completely different universe just because someone, somewhere, has altered the timeline somewhen.
I'd rather use... I don't know, planar shifting. Or instantaneous creation of a quantum-entangled clone at the destination point. Or consciousness transfer in a host body... but having to consider the myriad headaches of backwards time travel ? I have enough trouble keeping my setting in one piece as it is
More seriously, FTL travel explanation is best left as a consequence of Clarke's third law.