Spanish has 3 types of verbs, ar, er, and ir. French has 3 types: er, ir, and re. It looks like French shifted the verb to the right phonetically (if Spanish had a 4th re category, and I mean the vowels a e i o u). I don't speak French but I do speak Spanish occasionally at home. Latin had ar-like verbs too. So, why doesn't French?
French shifted the Latin vowel a to e in this context. This isn't a change that occurred only in verbs, but in all kinds of words: for example, the adjective cher comes from Latin carus, and the noun mer comes from Latin mare.
The general sound change is that Latin a in a stressed open syllable (basically, a followed by a single consonant and then an unstressed vowel) became French e (sometimes spelled ai). So the Latin infinitive ending -are became the French infinitive ending -er, and the Latin participle ending -ata became the French participle ending -ée, the Latin second person plural ending -atis became the French second person plural ending -ez, and so on.