Poule mouillée (lit. “wet hen”) is close: it means a person who lacks courage. It isn’t as widely applicable as chicken: you can’t use it as an adjective, and it’s not as natural as in English to use it as an interjection (though you can say “Espèce de poule mouillée !”, which is roughly equivalent to “You [are] chicken!”). It is usually constructed as “X est une poule mouillée”.
For example, a child might launch a race and taunt the other children by saying “le dernier arrivé est une poule mouillée”.

Where English children would shout “Chicken!”, I think French children would shout “oh, le peureux”. Another childish phrase that’s close is “t’es pas cap’” (short for capable), meaning “you don’t dare” (and hence can translate “I dare you”).

If you want to be rude while talking to a really close friend you could say “tapette” or “t’es une tapette !” which also stands for gay.

Don’t use that if that person is actually gay, that would really be homophobic.

Example:

— On va courir ?
— T’es fou il pleut !
— Tapette !

There is a wonderful film starring Marion Cotillard called (I think) Jeux d’enfants, in which two kids play a game of chicken throughout their lives. The expression they use (I think) is ‘cap pas cap‘. The English title of the film is ‘Love Me if you Dare’, so you get the feeling.

There’s another (mostly childish but not only) slang term that hasn’t been mentionned yet :

T’es un trouillard ! / Oh, le trouillard !

It’s very commonly used, and never to refer to someone with a “legitimate” or understandable fear. Its use implies that the scare is clearly disproportionnate to the real threat.

(However, let’s note that it fails to match the use of chicken in the expression to play chicken.)

t’a la frousse ? means “are you (too) scared to do it ?

I noticed that recentely more and more people (me included) started to use the word
” canard ” ( = duck ) exactly like english people use “chicken” , to mean that someone is not very brave in funny slang.

It’s dated and probably more “cowardly” and less funny than you wanted, but the “faux-ami,” “Capon/(caponne)” (without the “H” in “chapon“), works as both an adjective and a noun to communicate the idea of “a chicken/poulet (the animal) being afraid” in one word.

Though regional and by no mean used throughout the Francophony, pissou is used in Quebec for this purpose, and while poule mouillée is well understood too (and I’ll agree it is figuratively closer to chicken), it is not as commonly used here. It is to be expected that slang will differ wildly from region to region, and I agree that in any case, poule mouillée will be a very good choice.

But in a Quebec setting, and if the aim of the translation is to sound natural and native, not necessarily to keep the hen, pissou could be a very appropriate choice.

According to this article, the word came into French from the Langue d’oïl, and originally designated someone that needs to pee (pisser) often, or also a child that still pee in bed. This acceptation is dated in all regions of the Francophony, but a regional acceptation similar to what chicken is in English eventually emerged in Quebec¹, and is still widely used up to this day.

_{¹ I tend to think of it as a claim that in front of even a small danger, the pissou pee himself/herself, but I could not back it up with any type of document, so it remains open as to how it actually came into being.}

Here is an example from Le cahier rouge of Michel Tremblay, Quebec’s most famous contemporary writer, putting in the mouth of a drag queen why he’d rather dress as a lady than as a man:

Me voyez-vous d’ici ? Habillée en bûcheron avec les baguettes en l’air ? Le cul trop serré dans le seul jean que j’ai ? Épilée ? La queue de cheval sur l’épaule ? La petite démarche gondolante ? En gars, j’ai l’air fif; en fille, j’ai un peu plus l’air d’un être humain… J’me suis fait assez taper dessus quand j’étais à l’école pour m’enlever toute envie d’essayer d’avoir l’air d’un gars. Quand chuis en fille, je peux me défendre, y a rien qui me fait peur; pas quand chuis en gars. Quand chuis en gars, chuis un pissou, rien d’autre.