The Jumu`ah prayer does not require a bath to be valid. This is a matter of scholarly agreement. The eminent jurist Ibn Rajab says: "There is full agreement that a bath is not a condition for the Friday prayer's validity. The prayer is valid in any case."
However, taking a bath for Friday is – at the very least – strongly recommended. This is the ruling of all four schools of thought.
Some scholars even say that it is obligatory to take a bath on friday. To say that it is obligatory does not mean that it is a condition for the Jumu`ah prayer. It simply means that neglecting to take a bath on Friday morning is sinful, like neglecting any other religious duty.
The Prophet (peace be upon him) said: "Bathing on Friday is an obligation on everyone who has reached sexual maturity." [Sahîh al-Bukhârî (879) and Sahîh Muslim (846)]
He also said: "If any of you finds it to be Friday, he should take a bath." [Sahîh al-Bukhârî (877) and Sahîh Muslim (579)]
These hadîth, taken on their own, indicate that it is obligatory to take a bath on Friday. The majority of scholars understand these hadîth to refer to Friday morning, though Mâlik differs.
If there were no other authentic hadîth on the matter, then we would say that taking a bath on Friday is indeed an obligation. However there are other authentic hadîth that indicate otherwise.
`A'ishah said: "The people used to engage in their various employments. Then when they went off to the Jumu`ah prayerr in the state that they were in, they were told: 'Would that you had taken a bath'." [Sahîh al-Bukhârî (903) and Sahîh Muslim (847)]
`A'ishah also tells us: "People used to go out on Friday from their homes and families. They would get dirty. They would sweat and become covered in dust. One such person approached Allah's Messenger (peace be upon him) while he was with me. The Prophet (peace be upon him) said: 'If only you people would bathe for this day of yours'." [Sahîh al-Bukhârî (902) and Sahîh Muslim (847)]
These hadîth state the reason for taking a bath. It is so that the people attending the prayer will be clean and not bring an unpleasant smell with them into the crowded mosque form their having worked and sweated all morning.
Moreover, these people were told "Would that you had taken a bath." This indicates encouragement, not obligation.
Samurah b. Jundub narrates that Allah's Messenger (peace be upon him) said: "Whoever performs ablutions on Friday, that is well and good. And whoever takes a bath has done what is better." [Sunan al-Tirmidhî (497), Sunan Abî Dâwûd (354), Sunan al-Nasâ'î (1379)]
Taking all of the evidence into consideration, I would say that bathing on Friday is strongly recommended and preferable, but not obligatory as a general rule. However, it is obligatory for those who exert themselves on Friday morning and work up a sweat and for those who generally have a bad smell when they do not bathe. For such people, bathing is incumbent upon them before they go to attend the Jumu`ah prayer. This is so their smell does not cause discomfort for others in the congregation. This is the reason that we find indicated in hadîth of `A'ishah.
It is worth repeating that even though we say it is obligatory for them to bathe before attending the Jumu`ah prayer, their prayers will still be valid if they neglect to do so.
For other people who are not in an unacceptable state of hygiene, bathing on Friday morning is an emphatic Sunnah (sunnah muakkadah).
This is the conclusion that Ibn Taymiyah arrived at in his Ikhtiyârât (30).
And Allah knows best.