The electricity cut out during Jumu’ah prayer and they were not able to continue following the imam

If that happened before rukoo’ (bowing) in the first rak’ah, then what they did was correct. But if that happened after bowing with the imam then they should have completed it as Jumu’ah, with two rak’ahs. 

Shaykh ‘Abd al-‘Azeez ibn Baaz Aal al-Shaykh was asked about a similar situation and he said: Whoever catches up with one rak’ah of Jumu’ah then is faced with a problem such as the electricity cutting out and the like, should complete it as Jumu’ah on his own, i.e., he should pray the second rak’ah then say the salaam, because in al-Saheehayn it is narrated from Abu Hurayrah (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Whoever catches up with one rak’ah of the prayer has caught up with the prayer.” One catches up with the rak’ah by catching up with the rukoo’ (bowing). The one who does not catch up with rukoo’ with the imam has not caught up with the rak’ah. Based on this, if the people mentioned in the question did not catch up with anything but the opening takbeer with the imam, then they should have prayed it as Zuhr. End quote. 

Majallat al-Buhooth al-Islamiyyah (61/83).