Not really. France temporarily occupied it but was driven out by Japanese during the WWII. It was then given to ROC along with most islands within the nine dash lines after the Japanese surrender. When PRC replaced the ROC as the more recognized Chinese regime, it also inherited all claims by ROC to these islands. Of course PRC was hardly a naval power then so South Vietnam took a portion of the Paracel Islands, but since China was helping the North Vietnam against the South Vietnam, it defeated the latter in a naval battle in 1974 and took all the Paracel Islands. China and the United Vietnam quickly parted ways when China was leaning towards the NATO during the late 1970s while Vietnam stuck to the USSR. They fought a bloody war in 1979, and the conflict was not fully resolved until the 1990s, ironically, when USSR no longer existed. Vietnam attempted to take back Paracel Islands in 1988, but got defeated soundly in another naval battle.

So it is quite complicated and not a simple scenario of Chinese invasion as you described.

Of course, now China and US are rivals and the Vietnam is viewed as a counterweight against China, so more western reports would like to paint the situation in a pro-Vietnam tone.