By holding my arbitration in Paris, am I obliged to conduct the arbitral proceedings with French arbitrators and lawyers?

No. For over a century, Paris has hosted many thousands of international arbitrations, many of which have no links with France. Parties have been and remain totally free to conduct their arbitrations in the language they wish, applying rules and laws of their choice, with arbitrators and lawyers of their choice. Moreover, the French arbitration community itself includes multilingual practitioners of many nationalities who are up to date on economic and political issues that can have an impact on the resolution of complex, transnational commercial and financial disputes.