The everyday past tense — auxiliary + past participle.

• avoir (present) + past participleThe basic structure of the passé composé: conjugate 'avoir' in the present, then add the past participle. Used for most verbs.j'ai parlé = I spoke / I have spoken
• j'ai mangéFirst person singular with avoir. The passé composé covers both English simple past and present perfect.j'ai mangé = I ate / I have eaten
• tu as finiSecond person singular: 'tu as' + past participle of finir (fini).tu as fini = you finished / you have finished
• il a venduThird person singular: 'il a' + past participle of vendre (vendu).il a vendu = he sold / he has sold
• nous avons parléFirst person plural: 'nous avons' + past participle.nous avons parlé = we spoke / we have spoken
• ils ont faitThird person plural: 'ils ont' + past participle. Note the irregular participle 'fait' from faire.ils ont fait = they did / they have done
• -er verbs → -éRegular -er verbs form their past participle by replacing -er with -é.parler → parlé (spoken)
• -ir verbs → -iRegular -ir verbs form their past participle by replacing -ir with -i.finir → fini (finished)
• -re verbs → -uRegular -re verbs form their past participle by replacing -re with -u.vendre → vendu (sold)
• faire → faitIrregular past participle. 'faire' (to do/make) becomes 'fait'.j'ai fait = I did / I have done
• prendre → prisIrregular past participle. 'prendre' (to take) becomes 'pris'. Compounds (apprendre→appris, comprendre→compris) follow the same pattern.j'ai pris = I took / I have taken
• voir → vuIrregular past participle. 'voir' (to see) becomes 'vu'.j'ai vu = I saw / I have seen
• avoir → euIrregular past participle. 'avoir' (to have) becomes 'eu' (pronounced like 'u').j'ai eu = I had / I have had
• être → étéIrregular past participle. 'être' (to be) becomes 'été' — but être itself uses avoir as its auxiliary.j'ai été = I was / I have been
• vouloir → voulu / mettre → misMore irregular participles: 'vouloir' (to want) → voulu; 'mettre' (to put) → mis.j'ai voulu = I wanted; j'ai mis = I put
• être-auxiliary verbs (DR MRS VANDERTRAMP)A set of verbs of motion and change of state use 'être' (not avoir) as their auxiliary: aller, venir, arriver, partir, entrer, sortir, monter, descendre, naître, mourir, tomber, rester, devenir, retourner, passer, and reflexive verbs.je suis allé = I went; il est venu = he came
• je suis allé(e)aller uses être. With a feminine subject add -e: allée. Past participle agrees with the subject.je suis allé(e) = I went / I have gone
• il est né / il est mortnaître (to be born) → né and mourir (to die) → mort are être-verbs with irregular participles.il est né = he was born; il est mort = he died
• il est tombé / il est restétomber (to fall) and rester (to stay) are regular -er être-verbs: tombé, resté.il est tombé = he fell; il est resté = he stayed
• Agreement: elle est allée / ils sont allésWith être, the past participle agrees with the subject in gender and number: add -e (feminine), -s (masc. plural), -es (fem. plural).elle est allée = she went; ils sont allés = they went
• nous sommes arrivés / elle est partieMore être-verb agreement: arriver → arrivés (masc. plural), partir → partie (fem. singular).nous sommes arrivés = we arrived; elle est partie = she left