Do I need to go back to India and apply for German Visa from there ?
No. As long as you have a legal residence in France, you can apply for a visa at the German Embassy in France.
Les citoyens d’Australie, du Canada, des États-Unis d’Amérique, d’Israël, du Japon, de Nouvelle-Zélande, de la République de Corée et du Royaume-Uni de Grande-Bretagne et d’...
No. While on H-1b status, you can only work for the employer that petitioned you for H-1b status. You are authorized to work only through 8 CFR 274a.12(b)(9):
(b) Aliens authorized for employment with a specific employer incident
to status or parole. The following classes of aliens are authorized to
be employed in the United States by the specific employer ...