create a calculation program that will be displayed by the browser

prompt() function returns the result as a string, and not as a number. So you must convert each to integer using parseInt(number). If you don’t do that, both your operator and the numbers are strings.

do {
    var calculChoice = parseInt(prompt("What do you want to do ?\n\n 1 - Addition\n 2 - Soustraction\n 3 - Multiplication\n 4 - Division"));
} while(calculChoice != 1 && calculChoice != 2 && calculChoice != 3 && calculChoice != 4);

console.log(calculChoice);

do {
    var premierNombre  = parseInt(prompt("entrez votre premier nombre"));
    var deuxiemeNombre = parseInt(prompt("entrez votre second nombre"));
} while (isNaN(premierNombre)||isNaN(deuxiemeNombre));