Litespud

When I buy stuff in Europe (I live in the US), it can go a couple of ways. If I order online for shipping directly to the US, the seller may offer with/without VAT pricing (usually does, in my experience), so I get the VAT-less price. If I'm buying in person (this is usually in Ireland), I pay full price to the seller, but I can present the receipts and my boarding pass to a Customs & Excise booth at the airport, and I get the VAT back in cash from the government. Not saying it doesn't happen, but the seller shouldn't be in the business of verifying that their product has left the EU, unless they're shipping directly to a non-EU address. Since you're shipping to a destination within the EU, they're likely obligated to charge VAT, since the item is no longer under their control, and they can't guarantee that is has actually left the EU. The way VAT works is that their suppliers collect VAT from Canyon, Canyon collects it from the next buyer down the chain etc, and then each link in the chain sends a check to the government. Canyon have already paid VAT, so they're not going to not collect it from you if they can't guarantee that the item has left the EU. If they issue a refund on your say so or on the basis of the docs you provide (and remember that they're not in the business of verifying export docs), but the government ultimately decides that the docs are insufficient, then Canyon will be liable for the VAT that they refunded to you, and I can't see them leaving themselves open to that liability.
There might also be a timing issue. As I understand in, you had the bike shipped to France so you could use it before shipping it to India - correct? The VAT refund system is supposed to allow you to export things that are for use outside the EU. At what point does a bike leaving the EU with a stopover in France become a "French" bike and no longer eligible for VAT relief?
It sucks that Canyon gave you incorrect info, but they're bike builders, and the customer service rep likely wasn't an import/export expert.