Can I go if I'm close to 180 days?

I am staying in Japan to learn Japanese, my goal was to stay 6 months then get a student visa to further my studies, but did not manage to get the documents done correctly. (I stayed there for 2 trips of under 90 days each)

I want to return there to further my Japanese.

It has not been 180 days yet but I am getting close. (maybe around 170ish)

Will I be able to return to Japan for another 3 months to study Japanese?

I heard somewhere that countries in the Visa waiver are not affected by the 180 day rule (French Passport). Does anyone have any experience with this? My Ideal plan would be to return there for 3 months then, leave and re enter for 3 more months so I can finish my Japanese course. Is this possible? Will I atleast be able to return for 3 months?

There is no such thing as a "180 day rule".

There is no rule how long you need to be outside of Japan before returning and getting a new visa waiver. And definitely you can return before 180 days.

Sorry, my post wasn�ft clear
I have only returned to my home for a short while
The 180 day rule refers to how long I could stay in Japan within a year
I have already been for two separate trips, totaling almost 180 days with short brakes in between

I heard an informal rule, mentioning that I can only stay up to a certain amount of time a year
Is this true?

There is no such rule. You can stay more than 180 days in Japan on tourist visa.
There May be some tax implications.

You were clear and so was my reply ( and others), there is no "180 day" rule.
Some people think there is and reference BS internet pages that someone's friend heard someone might have had a problem because of blah blah blah. But, according to the Japanese law and Japanese Government and all of their relevant departments and regulation, it is false.

Just to add some additional context to the question you should have asked:
If you are properly visiting on the temporary permit (it is not a visa and is not just for tourism - temporary stay), then if you do get questions at immigration then you will have no problem answering them. Things like where you are living, are you working, how much money do your have, proof of onward travel. If you have difficulty with anything like that or suggest that you are other than a short term visitor, then expect additional questions.