After the death of someone of our family, must we really wait 40 days before living normally, as they do in North African countries?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Mourning a dead person is for three days except for the wife who should mourn her husband for 4 months and ten days as Allah Says (what means): {And those of you who die and leave wives behind them, they (the wives) shall wait concerning themselves for four months and ten days).} [Quran 2:234] The Prophet also said: “It is not lawful for a woman who believes in Allah and the Last Day to mourn a dead person more than three days except for a husband, whom she should mourn for 4 months and 10 days.” [Al-Bukhari and Muslim]

What is meant by mourning in Islam – which is done by a woman - means avoiding adorning herself, like not applying perfume, kohl or the like. It does not mean changing one’s way of life, or the way of eating and drinking, and not cleaning the toilet; rather, it means not beautifying herself as already mentioned.

As for waiting forty days and changing one's way of life during it, then this is a rejected innovation that has been introduced into the Muslim land. Its origin is an old practice from the Pharaoh’s era known as “the forty (days)”. They claim that the soul comes back to the corpse after 40 days. It is for this reason that they put some belongings such as food, drink, ornaments, clothes and the like with the corpse. So, when the soul comes back to the body, it finds its belongings with him as they claim.
Finally, Muslims should stick to the Sunnah of the Prophet and avoid all kinds of innovations in the religion.

Allah knows best.