A PhD in Informatics vs CS?
It depends on where you are and more on the details of the degree. Many other places than France use some variation on Information *, rather than Computer Science. Denmark for one. Others as well. In the US an information science or informatics degree is more often closer to a management degree than a CS degree. 

However, details matter. Algorithms, Languages and Compilers, AI, and such will make it a CS degree whatever its name. 

However, if it lacks those but has courses such as Information Processing or Transaction Processing or Decision Support Systems it may be not CS but something related. 

Such courses as Database Management Systems could be in either, though a CS degree will focus more on the theory of databases and such things as Entity Relationship modeling. 

In the US at least it is a bit confusing. But the general idea is that a CS degree is more focused on theory and an IS (Information Systems) degree is more (but not completely) focused on practice. 

Careers can be built with either degree. 

However, I'm surprised that anyone would think biomedical information systems is somehow a lesser art. There are many very serious issues that still need to be resolved in such systems and such study should cover such "hard" topics as security and encryption. But, details matter. 

On the other hand, your advisor is correct in that to make progress in an interdisciplinary field you should start with a firm grounding in one or the other. There will still be a lot to learn, but the grounding in one will help you focus on what you need from the other.