Нужно повесить событие мыши на тег option JS

let body = document.querySelector('body'); 
let fontFamilyFunction = function() { 
  let select = document.getElementById('selectFontStyle'); 
  select.addEventListener("change", function() { 
    console.log(this.value); 
    if (this.value == "cursive") { 
      body.style.fontStyle = 'italic'; 
    } 
  }); 
} 
fontFamilyFunction()

<select id="selectFontStyle"> 
  <option value="choose option" disabled selected>Choose option</option> 
  <option id="cursive" value="cursive">Cursive</option> 
  <option id="fantasy" value="fantasy">Fantasy</option> 
  <option id="monospace" value="monospace">Monospace</option> 
  <option id="sansSerif" value="sans-serif">Sans-Serif</option> 
</select> 
<p>Test</p>