Because you are making an HTTP call to your server, it takes some time to fetch the data. Instead of setting events state directly, you should wait for the response of your HTTP call. Your code should be like this:

componentDidMount() {

    fetch(url)

        .then(Response => Response.json())

        .then(data => {

            let evts = data;

            for (let i = 0; i < evts.length; i++) {

                evts[i].start = moment(evts[i].start).toDate();

                evts[i].end = moment(evts[i].end).toDate();

                this.state.evt1.push(evts[i])

            }

            this.setState({

                evt1: evts,

                prevEvents: evts

            })

        })

        .then(() => {



            console.log(this.state.evt1)

            const cachedHits = JSON.parse(localStorage.getItem('Evènements'))

            console.log(cachedHits)

            for (let j = 0; j < cachedHits.length; j++) {

                cachedHits[j].start = moment(cachedHits[j].start).toDate();

                cachedHits[j].end = moment(cachedHits[j].end).toDate();

                this.state.evt2.push(cachedHits[j])

            }

            this.setState({

                evt2: this.state.evt2

            })

            this.setState({

                events: [...this.state.evt1, ...this.state.evt2]

            })

            console.log(this.state.events)



        });

}

I also recommend you to have a catch block in your promise chain to handle errors.