Is the Friday prayer valid if the imam only recites Surat Al-Fatiha instead of delivering a sermon, and is it obligatory to search for another mosque?

Friday prayer is not valid without a sermon. In fact, according to the majority of scholars, two sermons are required, while the Hanafis deem one sermon sufficient. Evidence for this is the action of the Prophet (peace be upon him) and his saying: "Pray as you have seen me praying." The two sermons take the place of the two [omitted] rak'ahs. The Friday sermon has conditions and pillars. Among them, according to the Malikis, is that it should be at least what is considered a sermon. According to the Shafi'is and Hanbalis, these include: invoking blessings upon the Prophet (peace be upon him), exhorting to piety, and reciting a verse. The Hanbalis additionally stipulate the presence of admonition. Therefore, if the preacher limits himself to reciting only Al-Fatiha, the sermon is not valid.