In French (my mother language), in order to be polite, we use "vous" (the second person of plurial) when we talk to another person who deserves respect (a boss, a teacher, etc.) and "tu" for a close friend, a child, etc.). How do we do the same thing in English since there is only "you" for second person of singular and of plurial?
In most English dialects there is no direct equivalent of "tutoyer". It's very much more contextual.
In the area of England I live in (Sheffield) I still occasionally hear "thee" and "thou" but it seems to be a habit in decline.
As you've already noted, unlike in the Romance languages, in English there is only you for second person singular/plural. Therefore to connote respect, you might need to use additional words, while trying not to sound stuffy.
You could address the person by name (Mr./Mrs./Ms. Smith) and use slightly more formal speech.
Hi, Sherri, do you want something to drink?
Hello, Mrs. Smith, would you care for something to drink?
You can refer to a man as Sir, but it's trickier with a woman; many women feel offended (old) if you use Madam (or Ma'am), so you're stuck with Miss. However, if you say "madame" with a French accent, you can probably pull it off.
Politeness is achieved by using softening words such as would you mind and I wonder if..., using the passive voice (instead of saying, You said you would be here at one, you might say, It was agreed that you would be here by one.), using to + verb constructions (Can I take... vs. Might I be able to take... and other such nonsense, which you can find here, here, and here.
Courtesy is international. If you speak courteously in French,
you should have no problem with courtesy in English.
it is unlikely that you will experience any problems with other languages.
A plain offer: Do you want a cup of tea?
A more polite offer: Would you like a cup of tea?
A very polite offer: Shall I bring you a cup of tea?
An extremely polite offer: Would you care for a cup of tea?
A plain request: Can you close the window, please?
A more polite request: Could you close the window, please?
A very polite request: Would you mind closing the window, please?
A polite (and slightly hesitant) request:
I was wondering if you could close the window? If you didn't mind.
The most fundamental thing to remember is to remember to say please and thank you. Some people might consider the request: "Can you close the window?" as being too direct, and almost rude. If however, you tag on please at the end, that will normally suffice. Using the past tense, or modal verbs such as: could, shall, would etc. lends an air of hesitancy and allows the listener to either accept or refuse a request or an invite.
Simple answer, use a polite
tone in your voice (and maybe add a hint of sympathetic body language).