Idolizes and idolises are both English terms.
Idolizes is predominantly used in 🇺🇸 American (US) English (en-US) while idolises is predominantly used in 🇬🇧  British English (used in UK/AU/NZ) (en-GB).
In terms of actual appearance and usage, here's a breakdown by country, with usage level out of 100 (if available) 👇:
| Term | US | UK | India | Philippines | Canada | Australia | Liberia | Ireland | New Zealand | Jamaica | Trinidad & Tobago | Guyana | 
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| idolizes | 93 | 0 | 100 | 100 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 
| idolises | 7 | 100 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 
Below, we provide some examples of when to use idolizes or idolises with sample sentences.
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license.)