Re: using foreign words/phrases in writing
When foreign words are included in English text, they are italicized.
He had a certain je ne sais quoi aspect that I found utterly fascinating.
While all the ones in your second paragraph are so common that I wouldn't even italicize them, "explicite" is not a commonly used foreign expression in everyday English. If you can simply substitute in the English word "explicitly" I would do that, unless it's important to show the person was using a French word.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.