French is an exceptionally complex language. I offer here a brief summary of my French lesson today, in the hope that it will help anyone struggling with agreements.
Let's break it down.
J'ai cassé mes lunettes. - I have broken my glasses.
No agreement at all. Lunettes is a feminine plural noun. (This will be important later.)
Mes lunettes sont cassées. - My glasses are broken.
The part participle agrees with the subject! An extra e and an extra s are added because lunettes is feminine plural. (I told you it would be important later.) Notice that the verb in this case is être.
So far, so good.
Now, there are a few irregular verbs in French that use être instead of avoir because of reasons that are really exciting if you're a linguistic nerd like me.
Working on the assumption that you're not, we'll move on.
Those few verbs that do take être also need to agree with their subject. Thus Je suis venu, because I am a chap, but elle est venue, because she is not. And elles sont venues because elles are all ladies and there is more than one of them, hence the addition of both e and s.
So far so good.
However, if we move the direct object of the verb in front of the verb, we agree the part participle. But not with the subject. With the object.
So let's imagine Yoko and John are talking.
J'ai cassé mes lunettes, she says.
Où sont les lunettes que tu as cassées? he asks in response. Where are the glasses that you broke?
First sentence: Avoir, object after verb, no agreement.
Second sentence: Avoir, object before verb, agreement.
Remember that sometimes we can replace the whole object with an object pronoun:
Où sont mes lunettes? - Where are my glasses?
Je les ai cassées. - I broke them.
Once again, object before the verb, agreement - even though it's avoir.
Now let's move onto way more exciting things.
Yoko and John are talking again, and Yoko's been in an accident.
Je me suis cassée la main. - I've broken my hand.
Poor Yoko. Note that cassé has an extra e not because la main is feminine but because Yoko is. Notice also that in French our body is not really ours: we hold it, as it were, at arms' length. See also je me brosse les dents, je me lave les pieds, and je me brosse les cheveux.
The conversation continues before dinner:
Est-ce que tu t'es lavée les mains? - Have you washed your hands?
Oui, je me les suis lavées! - Yes, I washed them!
John's kind of a controlling douche.
But: in the first we have an agreement with the subject, tu, who's Yoko and a girl. In the second, the agreement is with the preceding direct object les, which stands for les mains.
I've added direct to my litany because there's one more stop on the grammar train, and it involves direct and indirect verbs. Indirect verbs take a preposition, direct verbs just get straight up in your grill. Most communication in French is indirect: je parle à, elle téléphone à, ils montrent à while receiving sensory information and doing things is more direct.
We've only worked with direct verbs so far, so let's add in some indirects. Yoko, John?
As-tu parlé à ta mère? - Have you called your mother?
Oui, je lui ai parlé plus tôt. - Yes, I called her earlier.
What the what? Preceding object but no agreement. French is a funny old language.
The reason is because lui is not a direct object pronoun. It's indirect. Preceding indirect objects get no agreements, but preceding direct objects do.
So: Never agree verbs with an avoir auxiliary, unless the object comes before the verb - in which case agree the past participle with the object - unless that object is indirect, in which case do not agree with anyone, do not pass Go, do not collect £200. Unless it's Sunday, in which case all rules are reversed and we'll all play Mornington Crescent until someone wins.
Now just for fun, translate the following sentence: I washed my hands. I washed them and scrubbed them, spoke to them and broke them.