All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Before answering your question, it should be noted that what the Muslims do on Fridays should not be ignored by any Muslim as this is among the common and known rites of Islamic religion.
What the Muslims do on Fridays is:
They have a ritual bath (Ghusl), beautify and wear perfume, then go to the mosque and pray as much as they want before Jumu'ah (Friday) prayer. They read chapter Al-Kahf (the Cave) and other chapters or verses, or remember Allaah and send prayers on the Prophet . When the Imaam comes and begins his speech, they listen to his speech and then they all pray together two Raka's Jumu'ah prayer. After that they recite the designated supplications that are said after the prayer. Then they return to their homes.
As regards songs in general and Anaasheed (Islamic songs without musical instruments), they are not permissible on Friday. Regarding the ruling about songs in general, then this has already been discussed in Fatwas: 81239 and 81545.
Allaah knows best.