A patriarchate of Lutèce might not make much of a difference.
During IIRC the late 4th century, a patriarchate was established in Aquileia in northern Italy, and even though there was a short-lived schism between the Aquileian Patriarchate and Rome, this patriarchate was soon re-absorbed by Rome.
IIRC the title of Patriarch of Aquileia still exists, but it is little more than an extra title that the bishop or archbishop of Aquileia has.
And as a989chris already pointed out; there weren't that many Christians in northern Gaul at the time (not quite as many as in the area of the Patriarchate of Aquileia), so, unless this patriarchate would somehow become isolated from Rome and the rest of the Church, this patriarchate is even more likely to disappear, with the extra title of patriarch for the archbishop of Paris as its only remnant.