That approach has not been adopted in the conjugation of the verb in French ; the lexical root perdures throughout the whole conjugation with in some cases a change in a vowel or a consonant but not on the basis of an opposition between types of tenses ;

(for instance)

• faire : je fais (présent), je ferai (futur)
• peindre : je peins (présent), je peigne (subjonctif présent)

There is another particularity of the French verb, although it’s true for only a few verbs, and that’s the occurrence of missing forms, as in this case (paitre).

Aller is the obvious example, since it alternates between three stems, with a different one in the present and in the perfect (I also include examples in the compound past which replaced the perfect more or less completely):

Je vais ↔ j’allai

Je vais ↔ je suis allé

Être maintains the Latin stem change between sum and fuī:

Je suis ↔ je fus

Je suis ↔ j’ai été

And avoir‘s stem has attrited to nothing in the past participle and the perfect (it is preserved in writing as ⟨e⟩ but not pronounced), creating another alternation:

J’ai ↔ j’eus

J’ai ↔ j’ai eu