Your code is almost right, just missed some details. To set the min and max axis value you need to use the viewWindow:{min: , max:} dictionary inside the hAxis and vAxis, as follows:

    var chart2 =
        ui.Chart.image
            .series({
              imageCollection: lai_august_19_broadleaf,
              region: aoi,
              reducer: ee.Reducer.mean(),
              scale: 500,
              xProperty: "system:index"
            })
            chart2.setOptions({
              title: 'Mean LAI France broadleaf forest forest June-August 2019',
              hAxis: {
                title: 'Time',
                viewWindow: {min: 0, max: 6},
              },
              vAxis: {
                title: 'LAI',
                viewWindow: {min: 1, max: 7}
              },
            });