Yes, both processors support international payments with automatic currency conversion.
Stripe:
Accepts 135+ currencies
Automatically converts to your default currency (usually USD)
Currency conversion fee: 1% of transaction
You receive funds in your chosen currency
PayPal:
Accepts 100+ currencies
Option to hold multiple currency balances
Conversion fees: 3-4% above base exchange rate
Can choose to accept payments in specific currencies only
For your clients: They pay in their local currency, and you receive payment in your currency. The conversion happens automatically behind the scenes.