Double major in Physics and engineering for career safety
At least in Europe, and probably in the US too, physicists are highly considered in industry, the unemployment rate is almost a technical zero. Doing research is another different beast: there are not so many positions, and you have to fight for them. Also, Academia not a very lucrative career path: a first job for a physicist or an engineer in industry may grant them 3-4 times more than in grad school (depending on the conditions), and it continues onwards.

I see you are eager to study both degrees, which is commendable, knowledge never hurts. What you need to consider is the costs, both economical (can you afford the university?) and in effort (can you really do both degrees at the same time?). Both degrees are difficult, and will take a great emotional toll. 

Some universities offer double degrees, where you end having both titles, and the subjects are (hopefully) sorted and arranged in the most convenient way for the student. For example, in Physics and Maths you need linear algebra; in a double degree you would only take the courses from Maths, as the ones in Physics are a subset. If the university does not have this arrangement, you may find yourself doing the same subjects twice, that may lead to added frustration.

Another cost are the grades: doing two things means you cannot do them both so well. Some admission put hard thresholds on the grades, and they may or may not consider your second degree as a sufficient merit to lower it. On the other hand, and provided the grades are not very damaged, almost any employer will see it as a great CV boost and will make it easier to get an industrial job.

As a last advice: if you go for it, be aware of your limits and ready to drop one of them if things get difficult before it brings you down. A degree and a half is a merit, two three-quarter degrees are two failures.