I figured out what caused this behavior on my component, I was defining the height of the slide this way :
const heightCarousel = '80vh'
<Slider {...settings}>
<div style={{height:heightCarousel, background:'#F4CC67', padding:'15px 0', textAlign:'center'}}><h3>1</h3></div>
<div style={{height:heightCarousel, background:'#AA8326', padding:'15px 0', textAlign:'center'}}><h3>2</h3></div>
</Slider>
Instead of below, which lets React-slick defining the width automatically of each slide :
<Slider {...settings}>
<div style={{background:'#F4CC67', textAlign:'center'}}><div><h2>TEST</h2></div></div>
<div style={{background:'#AA8326', textAlign:'center'}}><h3>2</h3></div>
</Slider>
Note that you cannot define height inside a slide or you will get the same issue, but you still can play with padding to style your content inside.