Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.

Friday prayer has conditions to be valid, including: that it be prayed in congregation during the time of Dhuhr, that it be preceded by two sermons, that each of the two sermons fulfills its pillars, that it be held within a settlement of buildings, and that it be attended by forty individuals from those upon whom Friday prayer is obligatory. Imam Ibn al-Naqib al-Shafi’i said: "After fulfilling the conditions of prayer, the conditions for the validity of Friday prayer are six: that it be performed in congregation during the time of Dhuhr after two sermons, within a settlement of buildings, by forty free, adult, sane men who are permanent residents where the Friday prayer is held, not leaving it except for a need" ['Umdat al-Salik, p. 82].

The form of the prayer mentioned in the above question is not valid for Friday prayer due to the failure to meet more than one condition of its validity: it was preceded by a single moving sermon, whereas the condition for the validity of Friday prayer is that it be preceded by two sermons with their pillars. Furthermore, a traveler who departs before Fajr on a long journey is not among the people for whom it is obligatory; therefore, his presence is not counted [toward the forty], as it must be performed by forty of those for whom it is obligatory. Additionally, it must be performed within a settlement of buildings, and it is not valid to perform it in places other than areas of residence.

In conclusion, the Friday prayer is not valid according to the form mentioned in the above question because it was not preceded by two sermons, it was not attended by forty of those for whom it is obligatory, and it was not held within a settlement of buildings. Therefore, you must pray it as Dhuhr, and you have the choice between shortening it to two Rak'ahs or completing it as four. Your prayer of two Rak'ahs with the intention of Friday prayer is not valid, nor is the joining of 'Asr with it, because the validity of joining 'Asr is dependent on the validity of the first prayer. Thus, you must repeat it as Dhuhr, and repeat 'Asr as well. And Allah the Almighty knows best.