I’m not European, but I assume PhDs in Food are not the most common thing and are not offered by most universities. This answer is proceeding under that assumption.
Assuming that you are doing research in chemistry and developing the necessary skills and competencies to work as an industrial chemist, I do not think having a PhD that’s officially in “Food” will be a significant hurdle. There are a lot of things that you can get a PhD in, and it’s impossible for job postings to list all possibly relevant departments. This is why you will often see language like “PhD in X, Y, Z, or a related field.” Institutions are aware that there are all sorts of unusual official degree titles, and tend to not be very strict about only allowing people with PhDs in a short list of approved fields get jobs.
What is important is that your CV clearly indicates that you are a chemist. This means that you are a member of chemistry academic associations, publish in chemistry journals, and speak at chemistry conferences. It’s fine if you also do those things at food science venues, but it’s important that someone with no knowledge of food looks at your CV and says “ah yes, this person is a chemist.”
If you have members of the chemistry department on your dissertation committee, ask them for advice about positioning yourself as a chemist. The same goes for professors in the chemistry department who you collaborate with or who have expressed interest in your research. If you do not have any such people, that may be a sign that your current trajectory isn’t “chemistry enough” to be recognized as chemistry by the academic community.
Another good strategy is to look at recent placements for people with degrees in Food at your university. Do they get jobs at the kinds of places you want to be? If there are a variety of types of people in the Food program (food anthropologists, food chemists, food historians, etc) you should focus on the Food chemists specifically.