Breakdown of Toutes les marionnettes que j'ai vues danser ont plu aux spectateurs.
je
I
avoir
to have
à
at / to / in (general locations) / about (what one thinks about / reacts to)
danser
to dance
Questions & Answers about Toutes les marionnettes que j'ai vues danser ont plu aux spectateurs.
Why does vues have an -es ending even though it is followed by the infinitive danser?
This is the special rule for verbs of perception (like voir, entendre, sentir) followed by an infinitive. You make the past participle agree with the preceding direct object (here, que representing the feminine plural marionnettes) ONLY if that object is performing the action of the infinitive. Since the puppets are the ones actively dancing, vues takes the feminine plural ending -es.
What would happen if the puppets weren't doing the action of the infinitive?
If the preceding direct object receives the action rather than performing it, the past participle does not agree. For example, if you said "All the puppets I saw being made" (Toutes les marionnettes que j'ai vu fabriquer), the word vu has no agreement because the puppets are not doing the making; someone else is making them.
Why doesn't plu agree with the feminine plural subject marionnettes?
The verb plaire (to please) is conjugated with avoir here, and past participles conjugated with avoir never agree with the subject. They only agree with a preceding direct object. Since plaire takes an indirect object (plaire à quelqu'un, which becomes aux spectateurs here), there is no direct object for it to agree with, so plu remains unchanged.