Indian auto manufacturing has been one of the few bright spots on the factory landscape in the past few years, with sales of cars and utility vehicles almost doubling from six years ago, and Chennai and other cities booming from the business.

But proposals that are part of India's discussions on a free trade agreement with the European Union threaten to undermine those gains by giving European automakers an unfair advantage and hindering future investments in Indian manufacturing, according the Society of Indian Automobile...