Disclaimer: This isn't legal advice. I'm not a legal professional. If you want legal advice, hire a lawyer.
This is a quote from the Microsoft Font Licensing FAQs about the fonts that come pre-installed as part of Windows Vista, 7, 8, 8.1, and 10, which include Segoe Script.
Can I sell things I print from Windows or make using these printouts,
say a book, ...
Just use google to find a vendor that sells the font. The good thing is that almost no font designer would make a font available for free personal use when they do not also sell them. It is like providing a demo version you could say.
Then make sure the ...
Segoe + its variants are Microsoft's. They have enough power to bring home every penny+a hefty interest% in every possible case where something is available.
Do not believe some grey font download sites. Ask Microsoft or check their font licensing to see what they actually want and start to find an alternative, if you cannot see you can legally use the font ...
I'm not a lawyer, never have been. And this is not legal advice in any interpretation. You need to speak to an attorney to understand any legal ramifications this situation may present.
You need to contact the vendor to see if you can purchase a commercial license. It's doubtful anyone here will know for certain.
If this were to somehow happen to me, I ...
When you talk about a logo you have to consider-
what the client wants,
who the audience is,
what is the purpose of that brand
what kind of logo the opponents have ( to avoid copyright issues).
And the text-based logo is not only about fonts!!!
It has to be geometrically presentable and aesthetic too.
You have to consider subtle symbolic components, ...
You should focus on the product first, then think about the logo. If you think about it, people don't visit a website to see the logo, they visit the website, because it is useful.
About the logo ... it's alright but I think you should create a custom connection between the F and r letters, because now there is a gap there.
Notice how all lines are either vertical or rotated 45°. This image follow a regular square grid, so it's easy to construct manually.
Enter Edit > Preferences > Guides & Grid to set up the grid as you prefer. (Here I'm in a print document and have set Grid > Gridline every to 10 mm.)
Make sure the grid is visible with View > Show Grid.
I'd speak to a professional, established, licensing agent, not a bunch of designers on the web.
Even if an agent requires a fee, it may be well worth it. A simple web search can find licensing agents.
There are most likely a bunch of small things you'll never think of that an established agent will be well aware of and have the knowledge to negotiate more ...