In reality, free-market capitalism is not driven purely by profit. If so, people would never pass up a better paying job for a job they enjoy more. Individuals would always choose more work over more family time, and charities would never receive more money than what can be gained through tax credits.
Perhaps a better definition is an economic system based on maximizing individual utility. Not all individuals who choose to work in a free market system are motivated exclusively by money. In many cases, they are also motivated by a desire to make the world a better place, job satisfaction, family time, education, etc. All of these factors influence economic markets.
Whether Christ would or would not endorse maximizing profit is questionable. If money is the end goal, we read that the love of money is the root of much evil. But He certainly endorses personal progress, including such things as education, family relationships, and charity.
In my view, if everyone in a society were striving to live as Christ would have them live, a capitalistic society would be wildly successful at eliminating social classes, providing for the needy, increasing in knowledge and wisdom, and avoiding war and worldly vices. All of this would occur because of the individual choices of the people, not because of fear of government.