Sorry - late to this thread.
I would second much of what others have said. French and Spanish are both beautiful languages.
When I was deciding what to read at university more years ago than I care to remember, the imaginative choice everyone made for the future was Russian. Fat lot of use that would have been.

Now, again after the event, many say Chinese. Few were saying it until comparatively recently. I would second the reservations about Chinese, not just because it is VERY hard to learn, but because there are more fluent English speakers leaving Chinese universities than there are leaving English ones.
But they do not do it to learn English, but to learn American. America is the worlds largest economy, very likely to remain so (IMHO China is a busted flush), and the usefulness of the language is multiplied by the rest of the Anglosphere. So from a commercial point of view - being native English speakers, we have, to slightly misquote, already come first in the lottery of life.
Some of the Indian languages might be useful, but again they turn out enormous numbers of English speaking graduates.

For a slightly off the wall suggestion, I would put forward Greek. I have benefited all my life from reading Latin, which is a simply massive help when learning any of the romance languages. My biggest regret is that my school dropped Greek a couple of years before I joined.

Learning Greek would similarly open all the doors for the Cyrillic languages. What a wonderful prospect!

I passed on the chance to learn any two of the following languages in addition to French at my school - German, Italian, Spanish or Russian. I did Latin and Greek instead - Latin may have had its uses for the reason you mention, and there were only 5 of us in my Greek class so that was great, but apart from knowing the alphabet thus making it easier to read signs, etc. in Modern Greek when visiting the country, I cannot honestly say it has been of any use at all other than as intellectual exercise. If only I'd had a crystal ball I could have chosen Spanish instead and got a head start instead of having to start from scratch in later life!

Different strokes for different folks. My elder brother finds his schoolboy Greek gets him through most everyday conversations. (Mind you he did get an A at A level - smart *rse)

Not relevant because my 11yo didn't have the choice, as has been said before, but yes I'd say Latin IS worth studying if given the chance........ I still help win quizzes because of faded dusty but dusted-down remnants of latin lingering in the recesses of my brain!

Difficult one really both my kids did Latin and hated it. Dropping it the moment they could and just sticking with the compulsory French/German options. I suppose there has to be an element of self selection, no point in studying something you hate.

Sensible kids. There's a whole lifetime to study Latin, if they so choose. However at school it is better to concentrate on the core subjects that either provide the basis of further study, have some practical use in life, or provide easy marks. Latin doesn't tick any of those boxes.

ooh are we counting Latin?

my elder dd does Latin & I did a year or so at school - it definitely helps with the study of any of the romance languages - & I also find it helps me to understand the structure of language, too

Basis of further study and practical use - most West European languages - (But not Basque)! Medicine? Archaeology? Philology? History?

Easy marks? Well, like all subjects Latin IS easy - if you are good at it. And hard if you are not.

But the thread is about third languages so by definition not EASY subjects - (although I fundamentally disagree that youngsters should only study easy things).

You don't need to speak Latin to study West European languages, Medicine, Archaeology, Philology, or History.

There are other core subjects (Maths is the obvious one) that you really do need to be skilled at in order to go on to study a great many other subjects.

Well it's mainly about 3rd languages for school children, and my point is that school children have a limited time to learn a lot of things. Latin is simply not top priority. That's not to say it isn't useful - there a many subjects that are useful in one way or another - it's just that some are more useful than others.

Furthermore children are particularly good at picking up spoken languages, and childhood is the only opportunity you get to gain native skills in those languages. Since it's impossible to gain native skills in Latin it's a bit of a waste learning it at that age at the expense of another language. In fact I'd hazard a guess that a 40 year old might be more adept at learning Latin than a child anyway, since a 40 year old has a larger Latin-based vocabulary to draw from.

Actually, chaps, the thread is about a choice of third language for an 11 year old, between just two. French and German. Latin is interesting, as are all the other diversions, and I only mention this because either of you might have interesting thoughts on that one core question: French or German if native English and nigh-on bilingual Spanish?

Fiona - a difficult question really- I speak both, and Spanish, Italian and a few other polyglot bits.

I can honestly say that my favourite language (German) has been of little use, despite having run businesses in Germany amongst other places, and my least favourite (French) is of diminishing importance in the world. Except to me.

My point was that any guess (and that is what they are) as to the future importance or value of a language is just that - a guess. We do the best we can, but it often appears that we learn by our earlier mistakes, but take the wrong lesson from them. (I hesitate here, as having lived on three continents and in a dozen countries, the doorway that language skills have opened is a constant joy.)

But for someone to suggest that learning building blocks is a useless exercise is, to my mind, simply crass.

I am gone.

I already gave you my thoughts on French and German as a third language for a school child in an earlier post (I think specifying that it has to be an 11 year old school child is being a bit too precise though).

Nobody has suggested that (and I suspect you know it)

Good thread as my daughter (in Italy) is going to have to make the same choice next year when she also has to choose which type of high school (liceo) she'll be going to the year after.

In the end none of us know which way our children will go; I thought I was definitely going the German route at school & then college, only to finish up working in Burundi, where my French vastly improved & then Iran where I learnt Farsi (Persian), which to my mind is the most beautiful of languages.
I'd definitely look at class size, hours per week coursebook(s), teacher competence etc as well as which language.
I'd still go for French!!!
Will be interesting to follow your child's progress.