Print the full conjugation of a French verb

JavaScript (ES6),  507  504 bytes

Returns an array of 7 tenses, where each tense is an array of 8 forms.

(v,[a,b]=v.split(/(..)$/),g=b>'r'?2:b<'i')=>[...S='0123456'].map(x=>'je/tu/il/elle/nous/vous/ils/elles'.split`/`.map((s,n)=>(!n*/^[aehiou]/.test(a)?"j'":s+' ')+a+(x>2&x<5?g>1?'r':b:'')+[...S+'789ABCD'].reduce((p,c)=>(l=p.split(c)).join(l.pop()),'55e91D4D3D7/s//9eC0s00tBai72AA/âm5âtes/èr1/îm5îtes8r72AA9oC/55e8483/7DeDeDeB76e65ât6i46i367DeD5îtB7D8ssCn2s22t848327BDi4Di3DA/a9/4/3/8/i7en6Ass5e/4on3ez2Ai178s88t0Dai').split`/`[(n-=n>2,n-=n>5)+('0x'+'102433656777888A99CBC'[x*3+g])*6]+['sst'[~-n/2]]))

Try it online! (regular verbs)

Try it online! (grammatical disaster using the irregular verbs suggested in the challenge)

Retina, 2051 1891 bytes (UTF-8)

(.+)er$
je $1e0tu $1es0il $1e0elle $1e0nous $1ons0vous $1ez0ils $1ent0elles $1ent0je $1ais0tu $1ais0il $1ait0elle $1ait0nous $1ions0vous $1iez0ils $1aient0elles $1aient0je $1ai0tu $1as0il $1a0elle $1a0nous $1âmes0vous $1âtes0ils $1èrent0elles $1èrent0je $1erai0tu $1eras0il $1era0elle $1era0nous $1erons0vous $1erez0ils $1eront0elles $1eront0je $1erais0tu $1erais0il $1erait0elle $1erait0nous $1erions0vous $1eriez0ils $1eraient0elles $1eraient0je $1e0tu $1es0il $1e0elle $1e0nous $1ions0vous $1iez0ils $1ent0elles $1ent0je $1asse0tu $1asses0il $1ât0elle $1ât0nous $1assions0vous $1assiez0ils $1assent0elles $1assent
(.+i)r$
je $1s0tu $1s0il $1t0elle $1t0nous $1ssons0vous $1ssez0ils $1ssent0elles $1ssent0je $1ssais0tu $1ssais0il $1ssait0elle $1ssait0nous $1ssions0vous $1ssiez0ils $1ssaient0elles $1ssaient0je $1s0tu $1s0il $1t0elle $1t0nous avoîmes0vous avoîtes0ils $1rent0elles $1rent0je $1rai0tu $1ras0il $1ra0elle $1ra0nous $1rons0vous $1rez0ils $1ront0elles $1ront0je $1rais0tu $1rais0il $1rait0elle $1rait0nous $1rions0vous $1riez0ils $1raient0elles $1raient0je $1sse0tu $1sses0il $1sse0elle $1sse0nous $1ssions0vous $1ssiez0ils $1ssent0elles $1ssent0je $1sse0tu $1sses0il avoît0elle avoît0nous $1ssions0vous $1ssiez0ils $1ssent0elles $1ssent
(.+)re$
je $1s0tu $1s0il fai0elle fai0nous $1ons0vous $1ez0ils $1ent0elles $1ent0je $1ais0tu $1ais0il $1ait0elle $1ait0nous $1ions0vous $1iez0ils $1aient0elles $1aient0je $1is0tu $1is0il $1it0elle $1it0nous $1îmes0vous $1îtes0ils $1irent0elles $1irent0je $1rai0tu $1ras0il $1ra0elle $1ra0nous $1rons0vous $1rez0ils $1ront0elles $1ront0je $1rais0tu $1rais0il $1rait0elle $1rait0nous $1rions0vous $1riez0ils $1raient0elles $1raient0je $1e0tu $1es0il $1e0elle $1e0nous $1ions0vous $1iez0ils $1ent0elles $1ent0je $1isse0tu $1isses0il $1ît0elle $1ît0nous $1issions0vous $1issiez0ils $1issent0elles $1issent
je ([aeiouh].+)
j'$1
S`0

To the point implementation. Will try to golf it down from here.

Try it online.

Explanation:

Handle all words ending with er, with a 0 as line separator:

(.+)er$
je $1e0tu $1es0il $1e0elle $1e0nous $1ons0vous $1ez0ils $1ent0elles $1ent0je $1ais0tu $1ais0il $1ait0elle $1ait0nous $1ions0vous $1iez0ils $1aient0elles $1aient0je $1ai0tu $1as0il $1a0elle $1a0nous $1âmes0vous $1âtes0ils $1èrent0elles $1èrent0je $1erai0tu $1eras0il $1era0elle $1era0nous $1erons0vous $1erez0ils $1eront0elles $1eront0je $1erais0tu $1erais0il $1erait0elle $1erait0nous $1erions0vous $1eriez0ils $1eraient0elles $1eraient0je $1e0tu $1es0il $1e0elle $1e0nous $1ions0vous $1iez0ils $1ent0elles $1ent0je $1asse0tu $1asses0il $1ât0elle $1ât0nous $1assions0vous $1assiez0ils $1assent0elles $1assent

Handle all words ending with ir, with 0 as line separator:

(.+i)r$
je $1s0tu $1s0il $1t0elle $1t0nous $1ssons0vous $1ssez0ils $1ssent0elles $1ssent0je $1ssais0tu $1ssais0il $1ssait0elle $1ssait0nous $1ssions0vous $1ssiez0ils $1ssaient0elles $1ssaient0je $1s0tu $1s0il $1t0elle $1t0nous avoîmes0vous avoîtes0ils $1rent0elles $1rent0je $1rai0tu $1ras0il $1ra0elle $1ra0nous $1rons0vous $1rez0ils $1ront0elles $1ront0je $1rais0tu $1rais0il $1rait0elle $1rait0nous $1rions0vous $1riez0ils $1raient0elles $1raient0je $1sse0tu $1sses0il $1sse0elle $1sse0nous $1ssions0vous $1ssiez0ils $1ssent0elles $1ssent0je $1sse0tu $1sses0il avoît0elle avoît0nous $1ssions0vous $1ssiez0ils $1ssent0elles $1ssent

Handle all words ending with re, with 0 as line separator:

(.+)re$
je $1s0tu $1s0il fai0elle fai0nous $1ons0vous $1ez0ils $1ent0elles $1ent0je $1ais0tu $1ais0il $1ait0elle $1ait0nous $1ions0vous $1iez0ils $1aient0elles $1aient0je $1is0tu $1is0il $1it0elle $1it0nous $1îmes0vous $1îtes0ils $1irent0elles $1irent0je $1rai0tu $1ras0il $1ra0elle $1ra0nous $1rons0vous $1rez0ils $1ront0elles $1ront0je $1rais0tu $1rais0il $1rait0elle $1rait0nous $1rions0vous $1riez0ils $1raient0elles $1raient0je $1e0tu $1es0il $1e0elle $1e0nous $1ions0vous $1iez0ils $1ent0elles $1ent0je $1isse0tu $1isses0il $1ît0elle $1ît0nous $1issions0vous $1issiez0ils $1issent0elles $1issent

Replace all je followed by a vowel or 'h' with j':

je ([aeiouh].+)
j'$1

And finally split on zeroes, which basically replaces all 0s with newlines:

S`0

After which the result is output implicitly.

Charcoal, 488 276 bytes

Ｆ⪪§⪪”}∨>↓⁷8lυW!M\ηX↨%]ν÷g×D\﹪3}Þ1Xζ÷Ｓ¹.m×Ｋ⦄}.}◧TI¡νυOＡ×∨´ＴE…8λ→Ｙ×⁶⁰⟦αＬi↓↶⎚⦃ω>◧‴κv≦｜≕…K⊕Yλ⎇＆✳⍘ςθＡ⪪@₂)¦Hg@»‽Ｈ2.⁵÷-⁸n¬u⊘¡″βEＮ≡x↔÷Wyⅈ(Ｊ\`﹪◨⁸｜|kU_ ←%Zσ¤«⊟Ｑ§!χ⁰⸿¤:\`α´↖±↔5À⊗I¡o⊞⁵cp✳ιg«“/_$↖↧↧⪫,↗A”¶¶⌕er§θ±²¶Ｆ⁶Ｆ⎇›№aehiou§θ⁰κ⟦j'⟧⁺⪪§⪪”↶↥ζ⊟pW↔,⦄≡ＷA→÷⪫$Ａⅉ⟦v⎇” 궦 «λ…θ⁻Ｌθ²⭆§⪪ι κ§⁺âèîμ⌕AEIμ⸿

Try it online! Link is to verbose version of code. Explanation:

Ｆ⪪§⪪”...”¶¶⌕er§θ±²¶

A very long compressed string is split into paragraphs, each paragraph representing the endings for a particular verb ending. The appropriate ending is selected depending on the second last letter in the verb. The paragraph is split into lines representing the endings for each tense in turn. The tenses are then looped over.

Ｆ⁶

Loop over the three persons and their plurals.

Ｆ⎇›№aehiou§θ⁰κ⟦j'⟧⁺⪪§⪪”↶↥ζ⊟pW↔,⦄≡ＷA→÷⪫$Ａⅉ⟦v⎇” 궦 «

Loop over the pronouns for those persons (third person has two genders), but special-casing ["j'"] where necessary.

λ

Print the pronoun.

…θ⁻Ｌθ²

Print the verb stem.

⭆§⪪ι κ§⁺âèîμ⌕AEIμ

Print the suffix, but translate AEI to âèî as Charcoal can't compress accented letters.

⸿

Start a new line.