Additional questions if you're willing/able:
EDIT: Apparently these are bigger stumpers than I had anticipated! Can anyone shed some light as to why these are difficult questions to answer? Are there any mods/experts here who specialize in the Baroque period in France? At this point I'm asking half for the kids and half for my own insatiable curiosity. Also, I thought up another question out of personal interest:
How am I traveling? I'm sure this would be determined by my finances/class/other factors. How much would a decent horse (get me from A to B) run me?
I also have audiences asking me to demonstrate my ability with a sword (I am very skilled in this) do I display my skills against an opponent, or is it possible to perform solo?
What is the etiquette in securing a "gig?"
I am very talented. What kind of living am I making? How much do I make in a typical night?
How long can I stay in town until my welcome is worn out?
How do I decide where to go next?
How are any of your answers changed if I am a woman?
It seems incredibly specific. Out of curiosity, why are you asking this question?
No effing clue, but I'm now equally curious and will upvote for visibility. Good luck dude/lass.
I do not specialize in the French Baroque. I specialize more in the first half of the century (1600-1650) in Italy, but I think this is closer than what anyone else has offered so far, so I will answer with what I can offer. (I am supposed to be studying and am procrastinating by answer this question so, despite the temptation, I will not go dive into a bunch of articles detailing 1670-1705).
A trend throughout music history: the popular songs of the common people were usually not notated--they were oral traditions, sung from memory, or improvised. Have you ever seen the song "Happy Birthday" notated? Lots of songs like that have come and gone throughout human history, and most of the most-sung ones have disappeared forever, because they were the best-known of their time. If everyone has it memorized, no one needs to write it down.
Most of the surviving music from baroque Europe is preserved thanks to noble or wealthy patrons who paid for its preservation. So whatever you would have been singing in a pub is probably not something we can easily access now. If you know any old French folk songs, one of them might be a start. Mudcat is a nice site for finding out about how old folk songs are. One old French folk song that comes to mind is "L'amour de moy" - it's older than the period you specified but could have still been sung. Usually, we don't really know details about what kind of music laypeople and musically illiterate people were singing. Sometimes shopkeepers or merchants would write song lyrics down in a book, but if they did that, it usually wasn't with notation.
If you are "very talented" and also TRAINED -- this is key -- then you're not singing at pubs and you're probably not just making ends meet. You're singing at courts, and if you're traveling, your services are being bought and sold by royalty and nobility. You probably have a primary patron who basically owns you. Everything in your life hinges on whether you stay in your patron's good graces. And if you are traveling, it is because that patron trades your services--possibly in diplomatic trades--with other nobles. In this case, securing a gig would be all about subtle hints and requests. It's likely the nobles at another court would request (via your patron) that you come, and any negotiations would need to be carried out obsequiously. The amount of flattery in these kinds of correspondences is extreme, and hints at the totally different class structure of this time and place. From our perspective today, it can be hard to relate.
If, despite your talent, you are not singing at courts, you might be performing as a member of a traveling troupe (doing less "high art" and more comedic/theatrical pieces). This kind of lifestyle was often frowned upon, though, especially among upper classes.
You also might be an opera singer, but most of the best opera singers also had a patron or three in their lives.
Some singers combined court, church/chapel, and/or opera gigs, but this could get complicated since the best singers usually had a noble patron with some ideas for what they should be doing. Again, I can't say the details for France at the time you asked (sorry). There was a very active Chapelle Royale in France at that time, though, and if you'd like to hear some music written for it, I love Couperin.
If you are a woman and singing as a soloist in public at a bar, you might be assumed to be a prostitute (or you might actually be one). You would not be upper class or even hanging out with the upper class.
My best guess for what music people might have made at a bar: dance music, above all. Remember, the bar was also the dance club. Next guess (that involves more singing): drinking songs, probably everyone at the entire bar singing together. Check out "Airs à boire" and "Airs à danser" for some ideas. Also maybe "Airs serieux" and "Chansonettes." You can google these terms with 17th century and hopefully something will turn up!
If they had a harp or lute at the bar and wanted to make some music with a solo voice, I would guess they'd do simple improvisations on a ground bass. You can check out Marais, Charpentier, and other French baroque composers for chaconnes, passacaglias, etc. These composers I just named were at courts and performing for nobility, so definitely considered more "refined" than what might happen at a bar, but the style may represent something of the contemporary aesthetic in France.