The American students thought that they being addressed on a first-name basis was a friendly gesture on the cashier's part. In fact, a majority of the students perferred the informality. On a couple of American students had a different reaction. The majority of the French students were taken aback by the cashier's use of their first name. This shows that the French prefer formality in a professional setting. Therefore, being polite and very respectful towards people you do not know seems to be extremely important for the French.

Question: How well do you have to need to know someone to begin to address them in the "tu" form? Are there specific people you will always address using "vous"?

I'm originally not from the US, and I think I was one of the anomalies on the U.S. response side.  In my country, it is rude to address people by their first name, unless the person is a friend, family, or a senior (older person) of some sort. 

How common is it for people to invite others to "tutoyer" them? 

Pour ma part, je pense qu'il est commun de vouvoyer dans le cadre professionnel et dans les administrations ainsi que toute personne imposant le respect. On a tendance à passer naturellement au tutoiement lorsque la relation devient "amicale" ou après un accord commun.

I guess that addressing people by first name in the US is more or less a social norm. It is a way of being friendly and make people feel welcomed. I'm orignally from China, and the way in which people address each other in professional settings is very similar to that in France. Respect and mannerism are the priorities. So I can understand the reasoning behind the French responses. Something interesting I saw on the American side is that some people feel that addressing one formally correlates with age. I feel somewhat the same way; if people addresses me formally, I would feel old and would prefer to be called just by first name. 

Are there any professional situations in which you'd prefer people addressing by your first name?   

After reading Celine's response, I'm curious about the type of relationship you have with your professors. At least half of the professors I've had at MIT request that their students address them by their first name or respond to an e-mail that I have sent using formal language (Ex. "Dear Professor Smith,...Sincerely, Kelcie Abraham,...etc.") using familiar or colloquial terms (Ex. "Hi Kelcie,...,From Joe,...etc."). We also have lots of opportunities to meet faculty members in an informal setting, like a reception or lunch organized by our department or an academic society.

What type of relationships do you have with your professors at Lille-3? Is it ever acceptable to "tutoyer" a faculty member? What sort of opportunities do you have to speak with professors outside of the classroom? 

I noticed one American student said that he would smile back and ask for the employee's number if the employee was a hot female. Would something like this ever occur in France? Also, I've always wondered how the French describe really attractive people in casual conversation. Here, I guess the most used term is "hot". What is it in France? Is it the same?

To comment on the responses on the French side and Mengwen's comment--does the use of formal language apply only to those in certain positions/occupations (your boss, the doorman, etc.)? Is it important to be formal also with older people (elder family members, for example)? The reason I ask this is because, I feel like in places like China, the use of formalities is emphasized as a sign of respect for one's elders rather than only a code of politeness.

Souvent, quand votre patron vous appelle par votre prénom en France, permettez moi de vous dire que "ça sent le sapin" comme le dit l'expression. Cette fausse familiarité dissimule souvent autre chose. (renvoi, grosse responsabilité gênante, etc). J'acquiesce au fait que le nom de famille est une marque de politesse et de respect envers ceux avec qui ont parle, même s'il peut aussi être une forme d'appui sur une critique (avec un beau môssieur ou madâme devant, l'accent devant être compris comme un renforcement du son).

Pour ce qui est du numéro de téléphone, ça ne marche pas trop comme technique de drague en France, à moins que la demoiselle connaisse également le montant actuel de votre énorme...compte en banque. :p

L'emploi du tutoiement dépend de la situation, mais en général dans un contexte de banque, cela ne se fait pas. Ce n'est pas normal d'appeler un client par son prénom (peut-être que s'il a 14-15 ans, ça passe). Moi je prendrai cela comme une erreur, mais si la personne continuait a me parler comme cela, je serais un peu embarassée quand même, pour moi, c'est vraiment un manque de politesse.

C'est tellement inhabituel qu'en effet, je verrais plutôt cet "oubli" comme une possible technique de séduction. En France, vouvoyer une personne dont on n'est pas proche fait partie du respect.

Généralement, en France, quand on appelle quelqu'un par son prénom, on le tutoie (sauf les professeurs d'université qui nous vouvoient).Il est impossible de tutoyer le professeur ou de l'appeler par son prenom.

On doit également vouvoyer les vieilles personnes. Par contre, il arrive souvent que des jeunes qui ne se connaissent pas, se rencontrent et se tutoient, du style  "Excuse-moi, tu n'aurais pas du feu?" (un briquet, des allumettes etc.)

Je me demandais, étant donné l'absence de tutoiement/vouvoiement, comment faites-vous, vous autres Américains pour juger si on vous parle en "tu" ou en "vous" ?

I tend to gage the formality of a conversation first from the context; for example, to whom are you speaking? Is it an older person, an interviewer, a professor, another student, a friend, a family member? In general I think that the guidelines for distinguishing between the "vous" and "tu" forms apply to American conversation. Next, I judge the formality based on the other person's tone of voice (Is it friendly or distant? Excited or detatched?), word choice (does he/she use colloquialisms or formal English?), body language (Do they lean in to you or keep a large distance? Are they standing or sitting while you are speaking to them?). These "clues" are usually sufficient to determine the degree of formality of the conversation so you can adjust your own speech accordingly.