All of the redefinitions have been done with the help of physics that was unknown at the time of the French Revolution, or at best poorly understood.
The meter was defined in 1960 using a spectral line's wavelength, and the second is now defined using a spectral line's frequency.
Spectral lines were first observed in the Sun's light by William Hyde Wollaston in 1802, and by the mid 19th cy., visible-light spectroscopy had become a well-established analytical-chemistry technique. Over the first half of the 20th cy., spectroscopy was extended across the electromagnetic spectrum, from radio waves to gamma rays.
The fixing of the speed of light in a vacuum, c, is justified by the great success of special relativity. It was developed to reconcile the conflict between Newtonian mechanics and Maxwellian electrodynamics, two theories that were otherwise very successful. In summary, while Newtonian mechanics has no built-in fixed speed, Maxwellian electrodynamics does: c, the speed of electromagnetic waves. In 1905, Albert Einstein showed that Newtonian mechanics had to be modified to fit, and that this modification included c as a sort of cosmic speed limit. A massive object can get closer and closer to c, but it cannot reach c. AE's teacher Hermann Minkowski soon showed that special relativity implies that space and time are part of a combined entity, spacetime, an entity whose geometry gives c as a dividing line between spacelike and timelike intervals.
Special relativity has been abundantly tested, both directly and indirectly, with the only known departures from it being due to gravity. AE came up with answer to that also in 1915: general relativity. That has also been abundantly tested, and it has also been very successful so far.
The fixing of Planck's quantum constant, h, is likewise justified by the great success of quantum mechanics. It was developed in the first third of the twentieth century, and it has been enormously successful in accounting for the behavior of everything atom-sized and smaller. Like the sizes of atoms -- that is a consequence of quantum mechanics. Quantum mechanics was initially developed for Newtonian-limit speeds, but by the mid 20th cy., it was successfully extended to speeds approaching c in the form of quantum field theory. Part of that was quantum electrodynamics, the quantum-mechanical theory of electromagnetism and the first part of the Standard Model of elementary particle physics.
Temperature, however, was always universal. The Celsius scale started off with 0 and 100 being the freezing and boiling points of water. The existence of an absolute zero of temperature was already suspected for some decades around the time of the French Revolution, though its value was not well established until the middle of the 19th cy. The kinetic theory of gases had been speculated about since antiquity, though it was in the late 19th cy. that it received a firm foundation from statistical mechanics. According to stat mech, temperature is essentially how much random energy a system has. The temperature-to-energy conversion factor is Boltzmann's thermodynamic constant.
However, temperature continued to be defined in terms of phase changes of water. In 1948, the triple point of water was defined to be at 0.01 C, and in 1954, it was defined to be at 273.16 K, making 0 C = 273.15 K. In 2005, this was clarified to be for water with the Vienna Standard Mean Ocean Water isotopic composition. But most recently, temperature was redefined in terms of energy by fixing Boltzmann's constant, something justified by the success of stat mech.
