Universality of free fall, famously depicted by Galileo's letting down various masses from the top of Pisa's tower, is a cornerstone of General Relativity to the extent that any alternative theory of gravity would almost certainly break that principle. This is why it is being tested by ever more sensitive experiments in the Solar system, such as the recent Microscope satellite. However accurate might these experiments be, they can only probe the regime of gravitational interaction that is available in the Solar system, which is very weak, and remain insensitive to some effects that may only arise in the strong-field regime. The latter requires a compact object, that is either a neutron star or a black hole, in a favourable orbital configuration.
Currently, PSR J0337+1715 is the unique millisecond pulsar found in a triple stellar system, orbiting two white dwarfs within an area comparable to the orbit of Venus. This configuration offers the opportunity for a dramatic improvement over previous tests, provided that accurate and regular timing of the pulsar can be achieved. This also requires the development of a new timing model solving numerically the relativistic three-body problem with great accuracy. In this talk, I will first review the state of the art of tests of the strong equivalence principle, and then report on the analysis of the high-quality dataset gathered on PSR J0337+1715 by the Nançay radiotelescope over the past 6 years. In particular, I will show how we could obtain the most stringent limit to-date on a potential violation of the strong equivalent principle in the strong field regime and discuss it in the framework of scalar-tensor theories.