> with this visa I cannot transit through any other Schengen countries as my point of entry needs to be France. Is that correct?

No.  You can transit through any Schengen country or countries on your way to France.  This is explicit in the [Schengen Borders Code](https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:02016R0399-20170407).

> Can I enter through Basel airport?

Yes.

> What I mean is, will the immigration authorities be representing France or Switzerland?

It doesn't matter.