I am also not a native English speaker, but I did not find Shakespeare hard to understand. The same happened for other non-native speakers that I know.
However, I am used to reading texts in many foreign languages and I am familiar with the etymology of many English words, i.e. with the evolution of their meanings in time. This is much more typical for non-native English speakers than for native English speakers and it might explain the difference.
In any case it is inappropriate to claim that Shakespeare's language is not Modern English.
The differences between Shakespeare's language and the current language are orders of magnitude smaller than for example the differences between French as taught officially and the language in which the novels of Frédéric Dard (the San-Antonio series) have been written (in the sixties and seventies of the 20th century). Those novels can really be hard to understand for native and non-native French speakers alike, before learning the specific slang used in them.
I am also not a native English speaker, but I did not find Shakespeare hard to understand. The same happened for other non-native speakers that I know.
However, I am used to reading texts in many foreign languages and I am familiar with the etymology of many English words, i.e. with the evolution of their meanings in time. This is much more typical for non-native English speakers than for native English speakers and it might explain the difference.
In any case it is inappropriate to claim that Shakespeare's language is not Modern English.
The differences between Shakespeare's language and the current language are orders of magnitude smaller than for example the differences between French as taught officially and the language in which the novels of Frédéric Dard (the San-Antonio series) have been written (in the sixties and seventies of the 20th century). Those novels can really be hard to understand for native and non-native French speakers alike, before learning the specific slang used in them.