Can you book a flight from place A to C, with a connection B which is in the opposite direction?

Domestic US only, but...

About 10 years ago, I had customers in both Las Vegas and Silicon Valley (flying to San Jose CA, south of San Francisco). I'm based in the Dallas area. The cheapest flight to San Jose was through Las Vegas (so I flew mostly west to Las Vegas, and then mostly west to San Jose).

But, the cheapest flight to Las Vegas, oddly enough, was through San Jose. So I'd fly West from DFW to San Jose and pretty much east to Las Vegas (both routes on American).

This is US/Canada:

About 30-35 years ago I was based in Montreal. I'd often fly to Atlanta (and then take a local flight). In Montreal, you pre-clear US customs before flights to the US.

The flight to Atlanta was through Boston. After MTL-BOS, just about everyone would get off the plane. There were only three of us left on the plane, including the guy in the aisle next to me, so we struck up a conversation. He was headed to Seattle. For some unfathomable reason, his travel agent (yeah, they were common in those days) booked him on Delta as YUL (Montreal) - BOS - ATL - SEA. They say that everyone changes planes in Atlanta, but that was the most insane routing I'd ever seen anyone follow.

And back to US-only

The most insane routing I've ever seen (the ticket was never purchased) was a colleague who was trying to get from DFW to Seattle. The (then new (early 2000s)) corporate travel website suggested going on Alaska Airlines, from DFW to Anchorage to Seattle. The return flight was also through Anchorage. The real kicker on that routing was that there are no directly Anchorage-DFW flights (in either direction) - they all stop in Seattle. So the first day would be DFW-SEA-Anchorage-SEA, and the return reversed that route. Oddly, it was actually about $75 cheaper than the flight he eventually purchased that skipped Anchorage in both directions.

I discovered last year that this even happens when you do not expect it.

I was scheduled for a flight from Phoenix to Oakland. I arrived earlier then expected and was offered an earlier flight.

To my surprise, there was a stopover in Portland...

This happened to me once.

It wasn't as extreme as your example, but it just proves that it happens.

I was in Cotonou, Benin and wanted to get back to Lebanon. The only flight I found was on Turkish airlines.

• We took off from Cotonou, stopped in Abidjan, Ivory Coast - this was just a technical stop, we didn't have to go down from the ariplane.
• Second stop was in Istanbul - a normal layover until the next flight.
• Third stop was my destination in Lebanon.

Basically, this is the path we took:

Another example I just remembered, was going from Lebanon to Madagascar. This time we went from Lebanon to Paris (Air France), then from Paris to Madagascar.

For your particular example, probably not unless you book the individual legs yourself, simply because it's so far out of the way and it's highly unlikely that there isn't a nearer airport with flights to Tokyo that you could fly to first.

In general though, it's not hugely unusual to go rather out of the way to get somewhere. I flew to Athens Greece (ATH) for work the first week of January this year from Dayton Ohio (DAY), both the outbound and return itineraries took me through O'Hare in Chicago (ORD) stateside and had the transatlantic legs of the flight originate and arrive there respectively, and that leg is about 90 degrees off bearing from what a direct flight to Europe would be (even more if you consider direct to Athens, but Athens is small enough and far enough east that you're likely to go through other places in Europe first if flying from the US). In fact a significant percentage of routes to Europe from Dayton (no matter where in Europe you're going) go either through Chicago or Atlanta (which is even more out of the way).

The common case here is flying long distance into our out of smaller airports, the norm then is to fly a short leg to a larger airport nearby, and then fly from there to where you're going (or to another larger airport nearby before flying to your final destination). Typically though, those connections going to larger airports are not going to be more than a few hours unless they're going in the desired direction anyway (for example, before the pandemic I was considering a vacation to Brisbane Australia this summer, and that would have been two long flights, one to get to a hub in Southern California, and then the transpacific leg to Brisbane from there).

This is very frequent in Canada. There are a limited number of international destinations from Halifax, Nova Scotia (YHZ). However, with the exception of Newfoundland, it is the most eastern major city in Canada. So, if you are looking to fly east from Halifax, you would fly west to a larger city like Montreal or Toronto, and then onward to your next destination, like Paris or London.

For example, there are flights like YHZ-YYZ-LHR which is 1300km in the wrong direction to take what would otherwise be a 4600km direct flight from Halifax to London.

I couldn't find a routing through Paris, but you can easily go from Delhi to Tokyo through Dubai on Emirates. That about 3.5 hours in pretty much the opposite direction.

Yes, and it is often done. Not often so extreme as in your case, but it is possible, and I think I saw this few times in questions in this site (people that did it, not as duplicate of your question)

Air France (as example, as in your question) has a hub in Paris. If they want to have you as their passenger, they must allow such fares. And baggage will be transferred, without need to pass custom. Sometime they required you to collect and to send it in transfer desk (just for extra control, and ask you few things): baggage condition could be different. But it is seldom (AFAIK not in Paris, not with the exactly same airline).

Going in opposite direction is often done (within a continent), but also from southern Africa to southern America: often it is convenient to pass from Europe.

In any case, I would also check a multi city ticket: you depart from one city (in India), and return to a new city (in Japan), and just a layover in Paris (maybe you can stay few days, "for free"). This is done a lot of time (think business travelers, so maybe just few hours in the "destination" airport).