<select id="country"></select>
<select id="city"></select>
const setOptions = (el, data) =>
el.innerHTML = data
.map(n => `<option>${n}</option>`)
.join('');
const countries = [
{ name: 'Германия', cities: [ 'Берлин', 'Бонн', 'Мюнхен' ] },
{ name: 'Франция', cities: [ 'Париж', 'Лион', 'Марсель' ] },
{ name: 'Италия', cities: [ 'Рим', 'Неаполь', 'Милан' ] },
];
const country = document.querySelector('#country');
const city = document.querySelector('#city');
setOptions(country, countries.map(n => n.name));
country.addEventListener('change', function() {
setOptions(city, countries.find(n => n.name === this.value).cities);
});
country.dispatchEvent(new Event('change'));
https://jsfiddle.net/ky4qbt8a/