Aren't there some past participles that don't ever agree? In 501 verbs, some are listed with their pp showing possible agreement and some not.

Hi Ann,

In the case of true 'intransitive'  verbs which by definition don't have an object , the past participle will not agree .

I am not sure that a list would help with this.

(N.B. some verbs can be both intransitive and transitive like servir, commencer ...)

Impersonal verbs as in expressions like 'il faut' or 'il y a' will always become 'il a fallu' and  'il y a eu' in the passé composé.

There is a group of verbs however which is interesting like coûter, valoir, peser, mesuser, courir...which express measure, quantity and duration  will be 'invariable' with 'avoir' even if the object precedes the verbs because the object is a quantity and answers to the question 'combien' and not 'quoi'.

e.g. 

Les millions d'euros que cette réparation nous a coûté...

Les kilos que ce paquet a pesé... 

Les heures que j'ai couru...

Hope this helps!