We say entrepreneur and entrepreneurship, what is the verb?

For the word entrepreneur and entrepreneurship, I would like to know the corresponding verb, i.e the action of doing entrepreneurship, i.e the verb that should fit in the next sentence :

To be a good entrepreneur you should ________ this and that project.

What would be the verb that shares the same root ? entrep... ??

You can undertake the project. (Or take it up. Gotta love idiom, no?) You can embark on a project, you can simply do a project.

Actually, an undertaking is a synonym for a project.

The strange thing is that the noun "undertaker" has gotten the specific meaning in English of a person that buries dead people - hence the use of the French for the professional.

This is a common source for (embarrassing) mistakes by foreigners. For a Dutchman for instance, it makes no sense consider that onder means under and nemen mean to take:

Onderneming -> undertaking (though it can also mean enterprise - same French source!)
Ondernemen -> to undertake
Ondernemer -> undertaker -> entrepreneur.

There is no exact verb for entrepreneur. Entrepreneurial is an adjective, and the two you listed, but no verb.

There's many verbs that could fit your blank: lead, command, undertake, drive, organize, manage, etc.

I'd use launch because it correlates to starting something up. When you start something you have to at some point launch (e.g. publish, release, deliver), then begins the cycle of shipping (e.g. to the value stream).

Launching seems to have the connotation of monetization baked in and that's an important distinction for entrepreneurs.

"I'm launching a venture to create plant-fueled cars."

Or, if you don't like "launch" I'd go with "starting" which relates to startups.

"I'm starting a company to create plant-fueled cars."