Yes, there is fee required by Cardano blockchain.
There are two main reasons why transaction fees are needed for Cardano SL: People who run full Cardano SL nodes spend time, money and effort to run the protocol, for which they should be compensated and rewarded. In contrast to Bitcoin, where new currency is created with each mined block, in Cardano SL, transaction fees are the only source of income for participants in the protocol. The second reason is the prevention of DDoS (Distributed Denial of Service) attacks. In a DDoS attack, an attacker tries to flood the network with dummy transactions, and if he has to pay a sufficiently high fee for each of those dummy transactions, this form of attack will become prohibitively expensive for him.