The short answer is yes: some categories of Jews were treated better by the Vichy authorities, but bear in mind that the Vichy government shifted considerably in its treatment of Jews over the course of the war, and the decisions made by local gendarmes were often chaotic and improvised on the spot. Initially, only foreign-born Jews were subject to resettlement, but in police raids and round-ups, large numbers of French Jews were also included.
Curiously, the Vichy government's definition of who constituted a Jew was somewhat broader than the one adopted in Germany in 1935, which meant that a broader segment of the Jewish population in unoccupied France than in occupied France was subject to mistreatment. Much of that mistreatment appeared (initially) to be benign: registration, identification, etc. In hindsight, it also served to expedite the subsequent process of concentration and deportation that was to ensue.
Certain categories of Jews, according to the Statut des Juifs of October 3rd, 1940, were technically protected. This included Jews with only one Jewish grandparent, or with two Jewish grandparents but who were, themselves, married to Christians. Even so, the authorities in occupied and unoccupied France competed with one another in the development of anti-Jewish legislation and even those Jews who were technically exempt still sometimes found themselves included in legislation that would deprive them of their jobs, their assets or their freedom.
Finally, being a Jewish convert to Christianity did not avail anybody. Nazi racial doctrine (as adopted also by the French) stipulated the biological character of Jewishness. While some people were able to receive assistance from the church, such assistance necessitated their going underground, changing their names and inventing an alibi. And even where people received protection or an exemption on the basis of their role within the community, Vichy authorities also complied when Nazi officials ordered arrests.
There is a great deal written on this subject, but I would recommend starting with Susan S. Zuccotti, "Surviving the Holocaust: The Situation in France". It can be found on pp492-509 of Michael Berenbaum and Abraham J. Peck (eds.), The Holocaust and History: The Known, the Unknown, the Disputed and the Reexamined (Bloomington, 1998).