It does increase serotonin reuptake (thus resulting in lower serotonin concentrations), but this is believed to be unrelated to its anti-depressant and relaxant effects. You can see a debunking here: https://en.wikipedia.org/wiki/Reuptake_enhancer
Tianeptine was found to simply be an opioid receptor agonist. In other words, it's just a mild opioid, sort of like codeine. Obviously, opioids and opiates can improve mood.
But it's a weak agonist, and the opioid receptors it targets are less implicated in the addiction and powerful euphoria associated with morphine or heroin. So, taken in low doses (the standard dose is very low), dependence and tolerance can remain low, and it can effectively improve mood over a long period of time. But increasing the dose will result in typical opioid euphoria, tolerance, and withdrawal effects.
Perhaps more importantly, it doesn't treat the root cause of depression in many people; it merely masks it. Sure, SSRIs often don't treat the root cause either, though for people with specific serotonin issues, they can. But an opioid or opiate is always just going to be a "layer" over your depression.
It also tends not to help people who struggle with avolition and lack of motivation or energy; it may even do the opposite, as opioids are wont to do.
But it will help with your mood. And it not treating the root cause is not necessarily a bad thing if it improves your enjoyment of life and your ability to function.
For many people, an SSRI will be more effective than tianeptine. For those who do not have any serotonin imbalance, tianeptine could be better.
I'm hopeful that as drugs unrelated to seratonin, norepinephrine, and dopamine start to show promise with depression, that we'll have a better picture of what's going on in the brain when people get depressed. IMO one of the missing pieces in severe depression treatment is what to do in the weeks it takes medications to take effect, if they even do; the current strategy seems to be "wait it out and if they're at risk of hurting themselves put them in a rubber room."
Wiki link for lazy folks: https://en.wikipedia.org/wiki/Tianeptine