What resulted from the Mughal Empire's trade relationship with European powers?

The answer is quite simple, colonization. Indeed, the French and the Portuguese had already established powerful business interest in India by the time the British came. They had started only dealing in trade activities but when local Mughal Rulers ruled against their economic interests their activities became political, fostering division and rebellion between Mughal principalities and kingdoms.

The British pushed the French away and established the East India Company as the dominant corporate force in India during the late 18th century (1757). This corporation ruled large parts of India with his sizable private armies. In 1858, after the Indian Rebellion of 1857, the company transferred all its political and military assets to the British Empire which assumed direct control of India.

The Mongols had a long tradition of supporting merchants and commerce. Early in his career before joining the Mongolian people, the Genghis Khan had encouraged foreign merchants. The merchants provided him with information about the neighboring cultures, served as diplomats and official merchants on behalf of the Mongols, and were indispensable to provide themselves with many goods, since the Mongols produced very few things. Sometimes the Mongols gave capital to the merchants, and sent them away in an orthoq (business partnership agreement). As the Empire grew, the merchants and ambassadors who carried authorizations and proper documentation received protection and refuge while traveling through Mongolian domains. A series of well-traveled and well-maintained routes connected the lands from the Mediterranean basin to China, and facilitated surface trade, and gave rise to fantastic stories of those who traveled by what was called the Silk Road. One of the most well-known travelers from the East to the West was Marco Polo, an equivalent trip from the East to the West was told by Mongolian Chinese monk Rabban Bar Sauma, who traveled from his home in Khanbaliq (Beijing) to Europe. Some missionaries such as William of Rubruck also traveled to the Mongol court, on conversion missions, or as papal envoys, carrying correspondence between the Pope and the Mongols in attempts to form a Franco-Mongolian alliance. However, it was rare for someone to travel the entire silk route, the merchants instead displacing the products in a kind of handrails, through which luxury goods were traded from one intermediary to the next, from China to the West, with what the final prices of the goods were extravagantly high.