We have already shared our opinions here. It's not a problem.

Thanks StCirq. It seems you travel a lot. So, you really think that there will not be a problem since it's just such an obvious mistake, that the conductor can understand by crosschecking the ticket and the passport? Do you think it might be more strict because it's from Basel to Paris? (another country)?

The conductors are not ogres.

I don't know how many times or ways it needs saying - it's NOT going to be a problem, whether it's an inter-France or international train. You have a picture ID, right? Do you resemble the picture? You have two names, right? They're the same on your ID and your ticket, right (though not in the same order)? You're fine.

Oooooookkkkkk!! It's just one of the trips of my dreams to Paris (first time) and I wouldn't want something like that to spoil it... Thanks a lot.

I think that KaterinaG is going to jail, just because she will look so guilty. Nobody else, of course.

Xa,xa! That was good kerouac! Goodnight!

It would help if they didn't translate the French terms for these names into such weird things in English, perhaps. "forename"! really, why didn't they just translate prénom into "first name". NOw I agree someone should know what forename means, but it isn't commonly used (at least in the US maybe that's my ignorance as that website is supposed to be used by British people, is forename commonly used in the UK? If it is, then it's fine.

I booked through the French website, utilizing my less then meager French and Google Translate for every word. I can be pretty neurotic in matters such as this one. Checked and rechecked every entry before I bought the tickets. How I messed the name up, I have no clue, since I did just fine last time I bought TGV tickets. Either that or I did not notice my mistake. In any event, it sounds that we all, including KaterinaG, will be fine.

Anna_Roz, I will let you know anyway, since it seems that my trip is earlier than yours!

BTW, I would also like to share with you the exact answer I received from TGV customer service desk, when I e-mailed them the mistake:
"...The tickets are not exchangeable etc. etc....But it depends if you are controlled by a sympathic agent, you can try to explain the mistake and presenting your passport, you'll be able to quietly continue your travel but I can't assure it will happen...".
Of course I was tempted to reply to them, and what if the agent is not sympathic???!! Anyway, I really don't believe it will be a problem, because it's actually common sense.

Just go quietly in that case. Try not to rattle the handcuffs as you are led off the train.

Yes, yes, I also liked that "quietly"...

I think they looked up "tranquillement" in the dictionary and found "quietly" as the first definition rather than "in tranquility."

I bought six IdTGV tickets and did the same thing on one of the six. I'm not losing any sleep over it. In fact, the one that is printed "backwards" actually looks correct as it has first name over last name, the way you'd say it. I can't imagine any conductor even saying anything about it. The names are correct, even if transposed, and the date of birth is listed correctly. They know that nobody else is going to show up to claim that seat.

I bought six IdTGV tickets and did the same thing on one of the six. I'm not losing any sleep over it. In fact, the one that is printed "backwards" actually looks correct as it has first name over last name, the way you'd say it. I can't imagine any conductor even saying anything about it. The names are correct, even if transposed, and the date of birth is listed correctly. They know that nobody else is going to show up to claim that seat.

I just realized a couple of days ago I had transposed names as well. My reply from TGV was that they were invalid and if I used them the conductor could fine me. All future correspondence has been ignored. Then I found a spot under cancellations that said if you want to change your time/date of departure/name/surname/birthdate it would cost 12 euro per ticket plus any difference in price between the original ticket and new. I was all set to inquire about this but from the sounds of the posts, I shouldn't bother. I was concerned they might have flagged my ticket. What would be the fine if the conductor charged you?

I'd like to know about anna_roz and KaterinaG travels with transposed names in the tickets. Any issue? Sympathic conductors? Any charge? As per the absence or further advice, it is supposed to having no problems at all...

I've never had any problem and never had my passport checked against a train ticket in France. No one has enough life to care.

Thanks bilboburgler.
In the meantime I have contacted the Voyages-nscf Team in the Facebook and they answered quickly, instructing me that I couldn't travel with wrong tickets and to contact Eurostar +33 892 35 35 39 (they have support in French and English). There, the operator told me there is no problem about that, in contrast to Voyages-sncf... Well, I trust in people here. I'll sleep in peace. If I would be fined, I'll sue everybody!!! ... kidding... actually I thank everyone :)