Spell out numbers in French

JavaScript (ES6) 318 321

Edit Bug fix (managing leading 0s) and golfed more

Credit for the camel case trick @Core1024

With input/output via popup

alert((n=prompt(),w='ZéroUnDeuxTroisQuatreCinqSixSeptHuitNeufDixOnzeDouzeTreizeQuatorzeQuinzeSeizeDix-septDix-huitDix-neufVingtTrenteQuaranteCinquanteSoixante'.match(/[A-Z][^A-Z]+/g),
u=n%10,s=u-1|n>80?d='-':' et ',n>99?'Cent':n<21?w[n|0]:n<70?w[18+n/10|0]+(u?s+w[u]:''):(n<80?w[24]:w[4]+d+w[20])+(n-80?s+w[n%20]:'s')))

As a testable function

F=n=>(
  w='ZéroUnDeuxTroisQuatreCinqSixSeptHuitNeufDixOnzeDouzeTreizeQuatorzeQuinzeSeizeDix-septDix-huitDix-neufVingtTrenteQuaranteCinquanteSoixante'
  .match(/[A-Z][^A-Z]+/g),
  u=n%10,s=u-1|n>80?d='-':' et ',
  n>99?'Cent':
  n<21?w[n|0]:
  n<70?w[18+n/10|0]+(u?s+w[u]:''):
  (n<80?w[24]:w[4]+d+w[20])+(n-80?s+w[n%20]:'s')
)

To Test In FireFox console or FireBug

for (i = 0; i < 100; console.log(r),i+= 10) 
  for (j=0, r=''; j < 10; j++)
    r+=(i+j)+':'+F(i+j+'')+", "; // specific: input is a string
F('100')

Test Output

0:Zéro, 1:Un, 2:Deux, 3:Trois, 4:Quatre, 5:Cinq, 6:Six, 7:Sept, 8:Huit, 9:Neuf,
10:Dix, 11:Onze, 12:Douze, 13:Treize, 14:Quatorze, 15:Quinze, 16:Seize, 17:Dix-sept, 18:Dix-huit, 19:Dix-neuf,
20:Vingt, 21:Vingt et Un, 22:Vingt-Deux, 23:Vingt-Trois, 24:Vingt-Quatre, 25:Vingt-Cinq, 26:Vingt-Six, 27:Vingt-Sept, 28:Vingt-Huit, 29:Vingt-Neuf,
30:Trente, 31:Trente et Un, 32:Trente-Deux, 33:Trente-Trois, 34:Trente-Quatre, 35:Trente-Cinq, 36:Trente-Six, 37:Trente-Sept, 38:Trente-Huit, 39:Trente-Neuf,
40:Quarante, 41:Quarante et Un, 42:Quarante-Deux, 43:Quarante-Trois, 44:Quarante-Quatre, 45:Quarante-Cinq, 46:Quarante-Six, 47:Quarante-Sept, 48:Quarante-Huit, 49:Quarante-Neuf,
50:Cinquante, 51:Cinquante et Un, 52:Cinquante-Deux, 53:Cinquante-Trois, 54:Cinquante-Quatre, 55:Cinquante-Cinq, 56:Cinquante-Six, 57:Cinquante-Sept, 58:Cinquante-Huit, 59:Cinquante-Neuf,
60:Soixante, 61:Soixante et Un, 62:Soixante-Deux, 63:Soixante-Trois, 64:Soixante-Quatre, 65:Soixante-Cinq, 66:Soixante-Six, 67:Soixante-Sept, 68:Soixante-Huit, 69:Soixante-Neuf,
70:Soixante-Dix, 71:Soixante et Onze, 72:Soixante-Douze, 73:Soixante-Treize, 74:Soixante-Quatorze, 75:Soixante-Quinze, 76:Soixante-Seize, 77:Soixante-Dix-sept, 78:Soixante-Dix-huit, 79:Soixante-Dix-neuf,
80:Quatre-Vingts, 81:Quatre-Vingt-Un, 82:Quatre-Vingt-Deux, 83:Quatre-Vingt-Trois, 84:Quatre-Vingt-Quatre, 85:Quatre-Vingt-Cinq, 86:Quatre-Vingt-Six, 87:Quatre-Vingt-Sept, 88:Quatre-Vingt-Huit, 89:Quatre-Vingt-Neuf,
90:Quatre-Vingt-Dix, 91:Quatre-Vingt-Onze, 92:Quatre-Vingt-Douze, 93:Quatre-Vingt-Treize, 94:Quatre-Vingt-Quatorze, 95:Quatre-Vingt-Quinze, 96:Quatre-Vingt-Seize, 97:Quatre-Vingt-Dix-sept, 98:Quatre-Vingt-Dix-huit, 99:Quatre-Vingt-Dix-neuf, 
"Cent"

Haskell, 390 bytes

b=(words"zéro un deux trois quatre cinq six sept huit neuf dix onze douze treize quatorze quinze seize vingt trente quarante cinquante soixante"!!)
a!b=a++"-"++b
f 0=b 0
f 71=f 60++" et onze"
f 80=f 4!b 17++"s"
f 100="cent"
f x|x<17=b x|x<20=b 10!b(x-10)|x>80=b 4!b 17!f(x-80)|m==1=f(x-1)++" et un"|x>60=f 60!f(x-60)|m==0=b(15+div x 10)|1<2=f(x-m)!f m where m=mod x 10
main=interact$f.read

Ungolfed

base :: Int -> String
--              0    1  2    3     4      5    6   7    8    9    10  11   12     13     14       15     16    17    18     19       20        21      
base i = words "zéro un deux trois quatre cinq six sept huit neuf dix onze douze  treize quatorze quinze seize vingt trente quarante cinquante soixante" !! i

hyphen :: String -> String -> String
a `hyphen` b = a ++ "-" ++ b

say :: Int -> String
say 0 = base 0
say 71 = say 60 ++ " et onze"
say 80 = say 4 `hyphen` base 17 ++ "s"
say 100 = "cent"
say x
  | x < 17 = base x
  | x < 20 = base 10 `hyphen` base (x - 10)
  | x > 80 = base 4 `hyphen` base 17 `hyphen` say (x - 80)
  | m == 1 = say (x - 1) ++ " et un"
  | x > 60 = say 60 `hyphen` say (x - 60)
  | m == 0 = base (div x 10 + 15)
  | otherwise = say (x - m) `hyphen` say m
  where m = mod x 10

main = putStr.say.read=<<getLine

Functional programming languages are quite suitable for this job.

Python - 344 (348)(380)(445)(537) bytes

Thanks to grc, Ray and isaacg for their help in the golfing process.

The code consists of the initial dictionary definition and a list comprehension that fills in the blanks with the junction of the dictionary's elements.

You can check the code online at repl.it

r=range
def f(a):b=a/60*10+10;d[a]=d[a-a%b]+(' et ','-')[a%10!=1or a>80]+d[a%b]
d=dict(zip(r(17)+r(20,70,10)+[80,100],'zéro un deux trois quatre cinq six sept huit neuf dix onze douze treize quatorze quinze seize vingt trente quarante cinquante soixante quatre-vingt cent'.split()))
[f(v)for v in r(100)if(v in d)<1]
d[80]+='s'
print d[input()]

My latest attempts to golf this code have been to forgo the generation process and with that reduction refine the function to just generate the requested number on the spot. However, since the 60 and 80's numbers need uncalculated elements, the struggle has been to create such a function while decreasing code.