You're welcome to submit a game in any language so if you would prefer to make it French that is OK :)
For the most part, your meaning is clear so you don't need to change it I think, but if you really do want the English corrections I'll do my best:
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White King: ... I'm afraid yes so...
B.K.: You don't won't move ?
Fine, as you wish. Coward.
W.K.: I can't hide anything to from you I suppose...
Well, good luck getting through the whole board without walking stepping on one of my little gifts !
Hehehehehe !
B.K.: ... Just wait and watch, I'm going to kick your coward's ass, coward !
*B.K: So... At least I can hear them ticking... If I concentrate enough I should at least know how many mines are around each cases (I'm not exactly sure what you mean here, perhaps "square" or "tile" or "place"? regardless, the main issue is when saying "each _____", the ____ should not be plural)...
"B.K.: I warn you, don't expect any kindness from I me.
B.K.: I'm not going to die now, all of my men count on me and my dear Queen...
I owe them to defeat you! (I'd say either "I owe it to them to defeat you!" or "I owe them your defeat!" The first is how most people would say it, the second is a slightly more calm/poetic way of saying it (I think it's more cool))
W.K.: Well... I've set the mines during the whole game so I'm not entirely sure of... Where they... Are... (this is fine, but "during the whole game" sounds a little odd to me after I played your game, the white king isn't doing anything during the game. perhaps you mean "across the whole board" instead? or just "I've set mines everywhere" for simplicity)
B.K.: Anything to say before I eat you just like all your former partisans ? (It's rare to use "partisan" like this, but it is not incorrect. Actually I quite like it :) )
B.K.: And so is your board ! Another land to had add to my kingdom !
B.K.: I am waiting for them, let them try !
You know pretty well how my ennemies enemies end.
Enough talking.
Prepare to die !
You fool, no one ever succeed such a task, and you're not going to be the first, I can swear it ! (Correct ways of saying this are "no one ever succeeds at such a task" or maybe "no one has ever succeeded such a task")
You've eaten the White King. No one is around to celebrate with you, but you've win won !
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In addition to the corrections, I should point out that in English we don't have chess pieces "Eat" one another, instead we say "take" or "capture". Do pieces "eat" one another when playing chess in France? I think that is really interesting!
also I played your game, I really like the idea :)