Charming!

Some (amateur) observations:

Is there a kink in the (inside) contour at the bottom of the bottom counter of /s/?

The fit otherwise is so tight, I wonder if you should bring the top of the first /s/ over towards the /h/ to help close that gap.

Another thing to consider is raising the ascenders of the /t/s a little to help them hold their own against those of the /f/ and /h/.

I also wonder if the stem of f should be thickened just a touch.

You have a really nice match of style and message here!

Aside from the fact that there's nothing fresh about the phrase "fresh start" I'd say it's looking...well, fresh. Have you considered matching the extended descender of the h on the last t? Just for balance. It might work, but it might be too busy?

I know you're trying to kern beautifully, but I think the 'a' in 'start' needs the rest of it's serif. Or maybe just a little hint of it? If you don't want to add it, the r's stem needs to be a touch thinner/tapered to look less odd with a missing foot.

(oops! double post)

^I think he meant the "r" in "start." The missing left part of the serif threw me off completely, it definitely needs to be there.

Overall, I think the logo looks a bit awkward. From afar, it looks like the "f" and "h" are randomly italicized, and the word "fresh" is visually way heavier than "start." I would say maybe leave the "f" but remove the tail/swash from "h." It's superfluous.

If you do want another swash element, consider doing a discretionary ligature on the "st" such as here.

Yes, I meant the 'r' not the 'a." Duh.