I have had great success cleaning carpets using Meguiars APC+.
It is very low sudsing, cleans really well, can be used carefully on dirty headliners and visors, and will not leave a water ring when it dries.
Since I do this for a living, I like to really, really, vacuum the carpets in several directions, using a brush to move the nap around and up and try to get as much of the deeply embedded dirt out first. It is going to take time, so be patient..
Then I will spray the Meguiars APC+ on the carpets, not too much (because you have to rinse and remove it), brush it in, and let it dwell, while I get my Extractor (which has already heated the water up) tool on the hose, and then go over the cleaned area, injecting a little hot water, extracting the displaced dirt and dirty soap out..
You need to think about how much water you are putting on the carpets and resist the temptation to flood it because "if a little is good - more is way better" - dont do that...
You dont want to get the water deep into the pad below..
You have to work very smart, quickly, and spend a lot of time extracting each square inch to get as much or all embedded dirt and crap out..
If you are willing to put in the time and have patience, and not get overwhelmed sometimes, you will be rewarded with very clean, clean smelling carpets..
When I get done with this, I always, always, have very dark brown to black water in my Extractor Recovery Tank - all that dirt and crap was still in the carpeting after all that dry vacuuming... This is the stuff that makes the carpets smell bad, and eventually grinds the carpet fibers to death..
And along with the rest of the extreme Detailing Cleaning inside, you will have an Interior that will look like brand new and smell very clean....
No nasty little trees, turtles, gummi-bears, frogs, etc., yucky things hanging inside the car or hidden under the seats...
Whenever I find these things in vehicles, I carefully collect all of them and put them in a big clear plastic bag that seals air tight, and return those nasty things to the Client, because they will no longer need to hide odors because I have removed all odor sources from the vehicle..
Just enjoy what a clean car smells like...
Good luck !
Dan F