First of all, you need a French lawyer to review your documents and to comment on French law.
France is a party to the 1958 New York Convention on the enforcement of foreign arbitral awards. They have an obligation to enforce agreement to arbitrate...and they will generally do so. If the agreement is so fatally drawn that it cannot be enforced, the court won't enforce it. If the agreement is a "little bit" defective so the court can fix it with an order, the court is likely to do so. The International Chamber of Commerce (which is a major international arbitral institution) is based in Paris and the courts of France are likely to want to promote arbitration.
If an arbitration clause was added at the last minute and you signed the document, too bad. The clause is in there.
If an exchange of documents created the "contract" and the arbitral clause was added at the last minute, that is considered a material change. If it wasn't explicitly accepted, it isn't part of the contract (see the UNIDROIT Principals, 3rd edition).
As you can see, you need to consult with someone familiar with your facts & french law....
I am admitted to practice in Connecticut and limit my responses to CT law.
This appears to be a matter of French law and I doubt anyone here can answer these questions. Is there some way this has anything to do with US law? If this is an issue involving French law, you will need a French attorney.
As an aside, I don't understand what you mean by "last minute" arbitration clause. Either the agreement had that clause at the time you agreed or it did not. It cannot just magically appear and bind you to its terms. Good luck on your matter.
This answer is for informational purposes only and is not legal advice regarding your question and does not establish an attorney-client relationship.
As pointed out already, if you entered into the "last minute" arbitration clause voluntarily it will be unlikely that the clause can be attacked as invalid. You may want to reconsider your position regarding arbitration since it can be a cost-effective way to resolve cross-border disputes and lead to a decision sooner than a civil lawsuit. An arbitration award is generally not subject to appeal and there are typically limited grounds to vacate an arbitration award. If necessary, the award can be enforced in court as if it were the court's own judgment.
This response provides general information only and does not create an attorney-client relationship. I am not admitted to practice in the State of Connecticut or France.