Translation is equally strange and challenging. It is also controversial. How far do you depart from the original language in order to accommodate the idiomatic flavour of the 'target' language. So in part it is a matter of ideology. If a story starts out as French and comes from that point of view, then I should argue that in the translation, there is merit in preserving a flavour of (in this case) the Frenchness of the story.
In your case, for example, "his carrots are cooked" will work fine. So long as you provide a context in which the point of your jeu de mots is clear, an anglophone reader will get it, and learn something into the bargain. There is a novel by the journalist, Gilles Paris, called L'autobiographie d'une Courgette, about a young boy with the nickname 'Aubergine' which is full of this sort of thing, because the boy keeps on getting the wrong end of the stick (and how would you put that in French?). So the nine-year-old boy's single mother is constantly muttering bitterly about her husband, Courgette's father, who apparently has run off with the next door neighbour's wife, to whom she refers as "la poule au voisin" (literally, "the neighbour's hen, except, as you know, 'poule' is also used to mean a whore or 'tart'). Well, Aubergine doesn't understand this and says
...je vois pas pourquoi il aurait emmené une poule au voisin pour faire le tour le monde avec. C'est bête une poule: ça boit la bière que je mélange aux graines et après ça titube jusqu'au mur avant de s'écrouler par terre.
... I can't see why he would have taken one of our neighbour's hens off on a world tour. A hen is stupid. It drinks the beer I mix into its feed and then staggers up to the wall and falls over.
How to translate the word 'hen' in such a case is a challenge. You can use 'bitch', but that is not perfect, unless you translate 'seeds' into 'feed'. There is, I am afraid, no easy way through this.
One author who wrote in both English and French was Samuel Beckett. But he tended to write the two 'from scratch', as I understand it. He did not try to translate in the conventional sense.
There is a notorious and very funny example of this problem in a television play by Tom Stoppard, called Professional Foul. It combines, as Stoppard's plays do, two unlikely groups of people going for an even to the same communist city of Prague: two philosophy lecturers, there for a philosophical colloquium, and two footballers there for a qualifying match. We are given part of one of the lectures, by an American philosopher of the school of linguistic philosophy. He is making a distinction between two senses of the expression to eat well, pointing out that it is ambiguous between: to eat in a well mannered and polite way, or to eat plenty of food. As this dull litany continues, the camera moves to the face of the French simultaneous translator, which is looking more and more puzzled and strained. He says nothing, but his expression says everything ... if you know French!. In French there is no way to translate what the philosopher is rambling on about, because in French there is no ambiguity: manger bien is one thing and bien manger is another.