Would calling a smaller firm "entrepreneurial" be offensive?

Not offensive but might come across the slightest bit condescending. Calling a firm entrepreneurial is kind of informal, or cute, or endearing language that should probably only be used by current employees. I would honestly roll my eyes if a candidate described my group as entrepreneurial to me, the same way I roll my eyes when a candidate tell me my group is “work hard play hard.”

I would suggest you rather say exactly what you mean. Are you saying the firm gives junior people more responsibility and earlier than other firms, and encourages junior people to get creative with problem solving, and tries to constantly improve rather than do things the way it’s always done, and focuses on growing fast to capture market share, and makes decisions quickly and efficiently? If so, then just outline those points or whatever points you’re trying to make without putting a cute label on it.