I disagree with the Ratatouille placement. The movie is intentionally stylised anachronistically, set in an idyllic version of working-class Paris that combines the aesthetic of the 1950s, 60s, 70s, and so on. However, Gusteau's will (which was signed one year prior to the events of the film) is dated here to June 23rd, 2004. This would place the events of the film around 2005.
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Additionally, in Inside Out, according to Riley's username on the Chat Master program shown in the film, she was born on January 22, 2003. Given that she is eleven during the events of the film, that would place the main events in 2014, the epilogue in 2015, and the events of the second film in 2016. I know it's contradictory to her alleged appearance in Finding Dory, but one can easily assume that is most likely just an easter egg.