Plural mark is indicated between parenthesis

Notes

A “note” is “une note”, plural “des notes”.

• 
  Breve: carrée(s) n.f. (seldom used, I just discovered it)
• 
  Semibreve (whole note): ronde(s) n.f.
• 
  Minim (half note): blanche(s) n.f
• 
  Crotchet (quarter note): noire(s) n.f.
• 
  Quaver (eight note): croche(s) n.f.
• 
  Semiquaver (sixteenth note): double(s) croche(s) n.f.
• Demisemiquaver (32^nd note): triple(s) croche(s) n.f.
• Hemidemisemiquaver (64^th note): quadruple(s) croche(s) n.f.

And so on, quintuple(s) croche(s), sextuple(s) croche(s), …

In “double croche”, “triple croche”, etc., the term “croche” is often dropped if it already appeared in the same rhythm. “A dotted quaver—semiquaver”, e.g., is referred to as “une croche pointée-double”, seldom as “une croche pointée-double croche”.

Rests

A “rest” is “un silence”, plural “des silences”.

• Breve rest: double(s) pause(s) n.f. or bâton(s) de pause n.m.
• 
  Semibreve rest (whole rest): pause(s) n.f.
• 
  Minim rest (half rest): demi-pause(s) n.f.
• 
  Crotchet rest (quarter rest): soupir(s) n.m.
• 
  Quaver rest (eight rest): demi-soupir(s) n.m.
• 
  Semiquaver rest (sixteenth rest): quart(s) de soupir n.m.
• 
  Demisemiquaver rest (32^nd rest): huitième(s) de soupir n.m.
• Hemidemisemiquaver rest (64^th rest): seizième(s) de soupir n.m.

And so on, trente-deuxième(s) de soupir, soixante-quatrième(s) de soupir, …

Tuplets

There is no general term to designate a tuplet. Tuplet, in french, are all masculine.

• Duplet: duolet(s) n.m.
• Triplet: triolet(s) n.m.
• Quadruplet: quartolet(s) n.m.
• Quintuplet: quintolet(s) n.m.
• Sextuplet (or whatever term you prefer): sextolet(s) n.m.
• Septuplets: septolet(s) n.m.

“Triplet quavers” are “un triolet de noires”.

Dotted notes

The dot itself is called “point (de prolongation)”. A “double dot” is “un double point”; “triple dote”, “triple point”.

A “dotted crotchet” is a “noire pointée”; “double pointed semibreve” is “blanche double-pointée”; “triple-dotted breve” would be “ronde triple-pointée”.