I see two different questions.
1. How can I book a Tokyo→Dubai→Paris flight?
A simple stopover such as this can be found and booked using the multi-city itinerary option on consumer sites like Hipmunk or Kayak. For more complex searches across multiple dates and connection points, I prefer to use the ITA Matrix Airfare Search, although ITA is not a travel agent and you cannot book tickets through them— you need to try to find the fare available on another website that handles bookings, like the airline's website or something like Orbitz or Cheapflights.
2. How can I find a Tokyo→Dubai→Paris flight that is comparable in price to a Tokyo→Paris flight?
No such flight may exist.
First, there are a fairly large number of airlines that can route you between Tokyo and Paris, especially with a connection. There is considerable competition, and therefore airfares are kept in check. Not every airline flies between Dubai and both Tokyo and Paris, however. With less competition, all else being equal, you will find airfares much higher.
Second, all airline tickets are not created equally, even if your seat and service may seem identical. Your travel is governed by the rules of the fare you purchased. Some fares may allow a stopover at no extra charge. For example, Icelandair will generally allow you a stopover between North America and Europe at KEF (their owners, a tourism company and an sovereign investment fund, have an interest in bringing tourists to Iceland). Other fares may allow a stopover for an additional surcharge. But other fares, especially the heavily discounted fares, may not allow a stopover at all. You would need to buy a more expensive fare or two separate fares for PAR-DXB and DXB-TYO, and that is the reason you get the pricier results.
So, look up the fare rules for the flight you have priced with the short layover. If the fare rules permit a stopover, you can work with a travel agent or with the airline to find availability for your preferred dates. If they do not permit a stopover, you have no choice but to purchase a more expensive ticket or purchase two separate tickets.
Workarounds include using frequent flyer miles, as noted in another answer, but seats may be difficult to come by unless you are flying very soon or have time to check often for flights in the future. Also consider that on most international itineraries, any stop of under 24 hours is considered a layover rather than a stopover. So, while a single day is obviously not as nice as a week, it would still give you enough time to get a glimpse of the city. I arranged a 22-hour connection IAD-JNB-DAR, which provided enough time for a quick tour of Soweto, the CBD, and some other parts of the city.