The reason all of the material you found about Fortran being old is because Fortran is old. You will find that many languages in physics are used simply because they are used. IDL, for instance, is used for things like image processing - it's often said among the department I know that uses IDL extensively that the only reason they still use IDL is because no-one has bothered to write the processing routines in MATLAB.
Fortran is good at what it does, but I wouldn't recommend it as a first language. It's messy, takes a while to get used to and will feel utterly illogical for a while. Once you're comfortable with setting programming aside as being something a bit abstract in your mind, Fortran is OK - the reason it's still used is simply because the things it can do, it can do very fast.
I also, certainly, wouldn't say you're reading above your level by learning programming - you mean you haven't dealt with any of those mentioned above as part of your course material? I was introduced to MATLAB in year one and had projects in it every year, as well as a bunch of others.
I would recommend you start with MATLAB. It's used extensively in physics, applied mathematics and engineering and is a great language to begin with. It's fairly easy to pick up, and many of the skills you'll learn in MATLAB are transferrable to things like C++. The tutorial system and built-in help are also pretty reasonable.