"Many people"
A subject is the noun of a sentence (animal, person, thing, etc.) that is performing the main action described in the rest of the sentence (predicate). When we talk about complete subjects we refer to the noun that performs the action plus all the other modifiers or adjectives that gives a further description of that noun.
In the sentence, "Many people" is the complete subject because "people" is the group performing the main action (to consider Basque a difficult language to learn) and "Many" adds detail of what quantity of people we are talking about.