Is fiber optic internet

Fiber isn’t completely noise free. 

But isn’t fiber optic the best and fastest internet?

If your streamer has a fiber optic input it’s worth trying. Other than that your fiber optic conversion is not going to help much if the last link in that chain is copper Ethernet. Using the best quality Ethernet cable and isolating your system from all the cheap, noisy switch mode power supplies that routers and switches come bundled with is what worked best for me in my system. Eliminates unnecessary clutter too. 

I am excited because as I write this a hole is been dug in  my yard to run new fiber to our house.  The internet provider is finally putting fiber in our area.  I should be able to get it in a few weeks.  Everything will be brand new.  I have had copper for years and it gives us problems constantly.  I assume this will very much improve the sound while also lowering my bill.

The question was specifically "fiber optic INTERNET." (vs a  fiber optic home network component)

That itself cannot theoretically offer any quietness advantage over Internet over copper.  However, theoretically, if a network was making any noise at all that could theoretically affect your DAC, then having fiber optic as the last leg into your streamer could theoretically result in a theoretically cleaner signal to the DAC, theoretically. But a good DAC should clean up any of that theoretical noise anyway.