Answer:
The European country that most likely monopolized the Indian cotton trade was Great Britain.
Explanation:
The 19th-century Great Britain was still an imperialist country. At that moment, however, it was prioritizing establishing colonies by means of free trade. It is interesting to notice the irony in the name, since the colonies were usually not free to trade with other partners at all. A colonizer would impose its presence and influence over an area or even a whole nation, forcing it to import its industrialized products and to export their raw materials. This is precisely what Great Britain did to India in the 19th century. India was absorbing textiles that Great Britain no longer had a market in Europe for. Great Britain, on the other hand, would import India's cotton, since India was no longer producing its own textiles.