In my experience (have been working as a software engineer for ~20 years -- damn, I'm old) the language is just one thing. It's more important to have a general understanding of design, algorithms, architecture and general programming principles. You may need to learn a new language on the job.
C is a useful language to know, as it's a base for other languages.
I'd recommend learning C (among other languages) and being prepared to learn new ones as knowing only one programming language these days does not get you too far.
Good luck!