As MikeJRamsey alluded to, one reason you're likely struggling with how all off this sounds, is that both sentences are untrue. International trade among nations is possible without a singular language. Therefore the word "feasible" is invalid.
The definition of "globalization" is also not precise. International trade is one thing that continues to become more globalized over time, but it is not synonymous with globalization. Various religions have also experienced increasing globalization. So has the Internet. So have weapons technologies. International trade is merely a subset of the things which are encompassed by the word "globalization".
What is true, however, and what the first sentence may be hoping to suggest, though imprecisely, is that where international trade exists, it tends to encourage use of a common language between trading partners. As an example, companies across Europe that transact with companies from other European nations tend to do business in English. Thus, I believe it is true that international trade, once it exists, creates a demand for the use of the same language, but not to make the trade feasible, only to make it easier.
Therefore, the first sentence is almost correct. The suggested rewrite is less correct since the word "need" is as incorrect as feasible was incorrect.
A rewrite that would fix many problems is: Increasing levels of international trade ultimately result in increasing demand from the businesses, citizens and governments of globalizing nations for a common language with worldwide trading partners in order to facilitate business transactions, employment and regulation.