Female cats who have not been spayed are fertile and sexually active all their lives. Therefore they do not go through the menopause. That is the short answer.
The spaying of female cats is called an ovariohysterectomy. It is a surgical procedure in which the uterus and ovaries are removed which stops subsequent oestrous symptoms in the female (going into heat). If oestrous symptoms continue it is because some ovarian tissue has not been removed during surgery. The remaining tissue secretes hormones allowing estrous behaviour to continue. It is called ‘Ovarian Remnant Syndrome In Cats’.
The menopause in humans is when a woman stops having periods and is therefore no longer able to become pregnant naturally. In the UK the average age for the menopause is 51 and most women experience menopausal symptoms, which can be quite severe and have an impact on day to day life.