I think it's
N'aie pas peur du futur, car je serai toujours là.
But du futur can be de l'avenir. I don't know.
Thanks for supplying a suggestion. It's a pretty good start, but you have options for several words.
I would indeed use avenir instead of futur here. Although futur is possible, to me it sounds a little stiff considering the association with grammar terms — whereas this is a more heartfelt sentence.
N'aie pas peur de l'avenir, car je serai toujours là.
Also, while toujours can mean always, it can also mean still in that sentence and with that placement, so you could go for a stronger pour toujours.
N'aie pas peur de l'avenir, car je serai là pour toujours.
Or, perhaps too poetically, à jamais :
N'aie pas peur de l'avenir, car je serai là à jamais.
Also, if your original sentence does indeed have "cause" instead of "because", then car could be a little too high a register. (In Europe, at least, it can be translated for and be matched with à jamais.)
N'aie pas peur de l'avenir, parce que je serai là pour toujours.
You could also delete car altogether; I think this borders on style editing, but it has a nice flow. Feelew writes below that having the causal relation spelled out seems to lose some of the warmth and focus attention on the speaker. That could look like:
N'aie pas peur de l'avenir ; je serai là pour toujours.
Finally, your English has "Don't live in fear" but the French you supplied says "Don't be afraid", so if you wanted to capture that first meaning you might try:
Ne vis pas dans la crainte de l'avenir, parce que je serai là pour toujours.
Ne vis pas dans la peur de l'avenir, parce que je serai là pour toujours.
As Stéphane points out below, the negation could also be plus ("anymore", "no longer"), if this word of comfort is given to someone who has already been living in fear up to this point.
Ne vis plus dans la crainte de l'avenir, car je serai là à jamais.
(P.S. Don't forget, as jlliagre mentions below, that if you're addressing more than one person you would use the vous forms: N'ayez pas or Ne vivez pas. I don't think this sentence is likely to be spoken using the polite vous, though, so if it's just one person I'd stick with the tu forms.)
Mix and match from among all these to get the right tone. :)
Disclaimer: I'm not a native speaker and invite any corrections if people disagree with my reading of the nuances or have better suggestions.