***** NOT A TEACHER *****
(1) Would it help you to better the sentence if I respectfully reminded you that "help" is one of those verbs that can be
followed by either a to-infinitive or by a bare infinitive?
(a) Thus: The dolls helped [to] spread Parisian fashions across Europe.
(2) You are, I believe, 100% correct. The sentence is: The dolls = subject; helped = verb.
(a) Of course, your listener/reader would ask "Helped what?"
(i) Then you would finish your sentence with a direct object. In this case, the direct object is an infinitive phrase.
(3) The dolls helped to create many needed jobs. (infinitive phrase)
The dolls helped the economy. (noun phrase)
(4) Joe: Parisian fashions have spread all across Europe.
Mona: Yes, I know. And the dolls have helped to do that. ("that" = to have spread all across Europe.)
Student or Learner