Why were the french welcomed by significant segments of the vietnamese population in the 1800s?

By the time the French invaded Vietnam, the local rulers had lost trust and respect among the local population.

The ordinary people and the peasants had seen a tough time with government interventionism and the failure of the Monarch, Tu Duc, to stop foreign aggression.

In the recent natural disasters such as droughts, floods, famines, and cholera outbreaks, the government had shown no resolve to actually help people. The natural disaster had lead to the deaths of nearly 1 million, with little to no support offered by the Monarchy in the form of housing, health, food etc.

Tu Duc' oppression of Christian missionaries also created a catholic community which was more than happy to support the French.

All these factors led to a significant population segment which actually welcomed the French

We can’t unless you list the “following” .

The answer is installation.