There are no formal arrangements in Ireland for clearing a French cheque. Any clearing arrangements are informal and based upon "correspondent banking". If your bank has a "correspondent bank" arrangement with the French bank, then clearing it might be fairly fast - if not, then there might be delays. Usually such cheques are accepted by your bank on a "for collection" basis - no funds will appear in your account until the funds are received from the French bank.
The position is likely to get worse rather than better in the future, as European countries pull out of cheques under the SEPA plan. SEPA = Single Euro Payments Area.