Universities in the US will certainly know how strong EPFL is. This is also true of ETHZ.
When I was a master’s degree student at Stanford, I knew at least one European student in the same program. I only remember him vaguely (this was a long time ago) but my recollection is that he was quite a good student (who also brewed interesting beer, which is part of why I remember him).
The one thing that I am not sure about is whether you will be able to get into a PhD program, or if you would need to get a master’s degree first. Master’s degree programs in the US are typically not funded – you have to pay and the cost is quite high at this point (it was much less expensive back when I did it). Your internships are likely to help you. Having only 3 years of university experience probably will not help. Getting funding for a master’s is probably more likely in Canada but I do not know how certain this would be for an international student .
Getting your master’s in Europe and then getting a PhD in the US is another possibility. PhD programs at top universities in the US typically are funded.
Taking the time to get your master’s degree in Europe and then applying for a PhD program in the US will also give you more time to think about what subfield of physics you are most interested in. Another option would be to work for a year or two or three and then apply to graduate programs.