[neximo64]

This is the basic Maastricht treaty. You cannot make EU law in France without France creating it not as EU law, but as French law. A SE or EU-INC would have to exist within this construct.

The only exception to a legal entity are the EU entities themselves which are supranational.

This is what most people don't understand with the EU, that there is a very specific process to create law and limitations on what it can do. It isn't like the US and the EU isn't a country. I may appreciate you might be European but even within Europe the detail with it is where it matters.

[bux93]

Article 288 of the Treaty on the Functioning of the European Union "A regulation shall have general application. It shall be binding in its entirety and directly applicable in all Member States." - for example, GDPR.

But even if this were implemented using a Directive (note: the SE is created in a Regulation, that's the link in my previous comment), this still would not mean that the law or the directive would necessarily need to require a company to be "sponsored" by a specific state - whatever that means. (Again, it would help if you'd define "sponsor" with a specific legal reference.)

And even then, Von der Leyen could have been talking about changing the TFEU treaty itself, which is ambitious but certainly not impossible. But again, I see no reason why this can't be done in a regular fashion, just like the already extant SE Regulation.