The fare you've quoted seems to be correct. I think the low fare is possibly because of a variety of reasons, that need to be considered together.

1. Other than AA and LH, only AI offers you a direct ORD-FRA connection - others will involve an extra stop.
2. You'll find very few non-Indians fly AI out of choice (which you get in F!). Since Indians are otherwise the principal customer base for AI, ORD-FRA is likely to be a light flight in F.
3. Except for connections that originate in India, the demand for ORD-FRA is quite small (virtually nil).

There may be more and finer reasons, but I think a combination of the 3 principal ones above should answer your question on the lower fare compared to other airlines. But then, AI isn't exactly the most passenger-friendly airline, though I think on purely international sectors and that too in F, their reputation has generally been good. I'd say go for it!