Equivalent of french CAPES or agrégation exam without having to teach

Note that if you pass the "agrégation" (i.e. successfully pass the exams) but don't teach after, then you cannot call yourself "agrégé de mathématiques" (as it's reserved for people who then teach) but you are allowed to say on your CV that you successfully passed the exams (I think it's "reçu au concours de l'agrégation", but not 100% certain). I shall not comment on the morality of potentially taking up a place in a competitive exam with limited number of places (the Mathematics one always has more places that admissible candidates, but still...). However it sounds like a lot of effort just to get a diploma.

The more traditional route is to get a "Licence" in another subject by taking online classes -- so there aren't any mandatory classes -- for the year of L3 at a nearby University (provided you can get an equivalency for the first two years of L1-L2), and taking the exam. It's not uncommon for students in Physics, Mathematics, or Computer Science for instance to get one or more degrees in related topics this way. If the secondary discipline is less closely related to Mathematics (say Philosophy or Ancient Languages), then it may be trickier to get the equivalency, although it's always easier to go from Mathematics to anything else than the reverse.

First, the CAPES and the agrégation are not "exams" in the sense of a final exam that grants a diploma if you get a minimum grade. They are civil service entrance examinations, in the sense that they are a competition between all applicants and the top performers get the job. Putting on your CV that you went to a job interview, got the job, and then refused it, is relatively pointless.

So to answer your question, no, there is no equivalent of the CAPES or the agrégation without the requirement to teach afterwards (if you take the job), because they are literally formalized competitive job interviews to become a teacher at a secondary school.

Second of all, merely getting the certificate/agrégation also does not prove that you are particularly competent, only that you outperformed enough other candidates to be in the pool of candidates selected to get the job. Since the state of the éducation nationale is so bad and the number of applicants so low, for the CAPES it basically means that you showed up and have a basic knowledge of the subject. For the agrégation, it means that you have an undergrad level of proficiency, pretty much.

The CAPES is a complete waste of time if you plan to have an academic career. It used to be that getting a very top ranking (say, top 10-20) at the agrégation in some subjects could give a boost to your early career as an academic. Nowadays, getting an academic job is so competitive that your research output will be enormously more important than some job competition you went to before your PhD. This is especially true since the agrégation (like most civil service jobs) is reserved for EU nationals, but academic job searches are largely international today.

The closest thing to what you want would be to get a license ("bachelor" for American speakers) in your field of choice. But again, I am highly doubtful that this will have any sort of impact on your future academic career. Anything you will do as an undergrad will be dwarfed by what you do during your master's degree and will essentially be forgotten as irrelevant. And what you did during your master's degree will essentially be forgotten after your PhD – only your research output will count. Even if you end up going out of academia, getting a license in a different topic would only be a very small boost to your CV after you get your master's and especially PhD.

The only worthwhile thing I can think of would be if you somehow managed to self-study a topic to the level of getting a master's degree without taking classes. But this is a feat that few can attain. And even then, you would need to prove that your diverse background will enable you to perform research at the interface of two different fields. It's not the kind of things you can learn in self-study books, to be perfectly honest.