Difficult cases of past participle agreement

There are actually a few cases where it's difficult to decide on whether a pronoun or noun phrase is the direct or indirect object.

Reflexive verbs that never take a direct object

There are a handful of reflexive verbs such as se rire, se moquer, se taire, s'apercevoir, se mourir that:

• Don't generally have a non-reflexive form that takes a direct object (rire and mourir are always intransitive; moquer as a non-reflexive verb is rare), or where...
• ...the non-reflexive usage doesn't very well explain the reflexive usage (apercevoir qch means 'to notice sth', but s'apercevoir (de qch) doesn't mean 'to notice oneself') and/or...
• ...never take a direct object (one would always say se moquer de qch, not *se moquer qch; mourir means 'to die', and se mourir doesn't make any more sense literally speaking than 'to die oneself' would in English).

So in these cases, it's arguable whether the reflexive pronoun is the direct or indirect object. In practice, you'll see variation in whether the past participle agrees or not with the subject of these verbs (and grammarians stating "rules" as to whether or not the participle agrees, but with little justification either way).

There are other cases where the non-reflexive verb never takes a direct object, but where it's clearer from the meaning that in the reflexive form the reflexive pronoun is the indirect object (and so doesn't agree with the past participle). For example, the verb plaîre always takes an indirect object in the expression plaîre à qn:

cette musique lui plaît
he likes this music
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So when used reflexively, the past participle remains invariable because the reflexive pronoun is considered to be indirect:

elles se sont plu à Nice
they had a good time in Nice
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The past participle of être

Consider the sentence:

je ne suis plus la fille que j'ai été(e)
I'm no longer the girl I once was
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What happens to the past participle? The answer is that être is considered not to take a direct object. Instead, its "object" is variously referred to as a predicate or complement (both quite vague terms). The bottom line is that the form été is considered to be the prescriptively correct one.

"les quinze jours qu'il a plu", "les 60 kilos qu'il a pesé"...

In these sentences, the phrases les quinze jours and les 60 kilos are not considered to be direct objects. In the first case, quinze jours clearly isn't "the thing being rained", and les 60 kilos isn't "the thing being weighed". So in these cases, the past participle doesn't have an agreement.

Contrast this with the following sentence:

voici les bébés que j'ai pesés
here are the babies that I weighed
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Here, les bébés is the direct object (the "thing being weighed") and so the past participle agrees.

Past participle followed by an infinitive

In the French equivalent of 'to see/hear somebody do(ing) something', French uses an infinitive for the second verb:

je l'ai entendue chanter
I heard her singing
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As you see, in this case the norm is for the past participle to 'agree' with the direct object (l') when it comes before the verb.

There is another similar-looking construction in which the infinitive in French is actually the equivalent of a passive verb in English:

c'est la chanson que j'ai entendu chanter
it's the song that I heard being sung
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In such cases, where the infinitive has a passive interpretation equivalent of English 'being ...ed', the norm is to not add an agreement to the past participle.

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