Lineage of a Person

Assalâmu ‘alaykum wa rahmatullâhi wa barakâtuh.

1) Is it correct that according to Islâm the origin (e.g. Turkish, German, Arab) of a person is defined *only* by the father and nothing else?

2) Example: Father is Turkish, mother is German and the child is conceived and born in France.
According to Islâm, what will the child now be considered? A Turk, a German, a French or a mix?

3)As far as I know according to Islâm the child in the above example would be considered a Turk, is that correct?

Wa’alaykum as Salām wa raḥmatullāhi wa barakātuhu,

The lineage of a person will be towards the father. Thus, in the example you mentioned, the child will considered a Turk.

لأن النسب للآباء (المبسوط للسرخسي
(289/27)

لأن النسب للآباء لا للأمهات وفيه حمل الزوجية على الغير فلا يصح
(الدر المختار617/5)