There were several other Asian countries with abundant resources, so why did the French choose to colonize Vietnam?
While there were many other places that the French might have wanted to colonize, there were not many other places in Asia that the French could colonize. Most of the rest of Asia was already colonized by the time the French started to colonize Vietnam.
There was a time when the French were more ambitious. For example, they had been involved in colonizing India, but were defeated by the British. But then the French were badly weakened by the Napoleonic Wars of the early 1800s. By the time that they were strong enough to think about imperialism again, most of Asia was already “taken.”
The British had India and Malaya. The Dutch had Indonesia. The Spanish had the Philippines. That did not leave very much for the French. The main thing that could be taken was the area that became French Indochina.
Thus, it is not really right to imply that France could have had its pick of lots of other countries to colonize. Vietnam was about the only thing left to colonize because other European countries had already taken so much of the region.
It is not correct to suggest that France chose only Vietnam to colonize. While Vietnam -- specifically, the 1954 battle at Dien Bien Phu -- marked the end of French rule in Southeast Asia, French holdings in that region also included Cambodia and Laos. A look at a map of what was called French Indochina shows the full extent of France's colonial conquests in Southeast Asia.
Additionally, while other countries, mainly the British in India, Malaya and Singapore, as well as Hong Kong and mainland China, the Dutch in Indonesia (the East Indies), and the Portuegese in India and China, all laid claim to vast resource-rich territories in Asia, the French holdings in Southeast Asia included great expanses of forests from which rubber was tapped -- rubber that provided the foundation for the French tire company Michelin. The Michelin rubber plantation was the largest and most prominent in Southeast Asia.
In conclusion, then, French imperial holdings in Asia, while hardly at the scale of the British, were substantial and valuable.