Zlatko Dalic's men could not face two tougher tests to start their campaign in League A, Group C as they go head-to-head with the European champions in Porto’s Estadio do Dragao before taking on the world champions in the Stade de France three days later.
Barisic, understandably, is relishing both games. He said: "I am looking forward to them.
Croatia coach Dalic echoed Barisic's words, telling UEFA.com: "Our opponents can't be harder. In the space of three days we will play away against the European champions and then the world champions.
"We respect Portugal and France, but we have a lot of trump cards and we will certainly try to break the negative run we have against both teams.
Barisic was interviewed for RangersTV after Saturday's 2-0 win over Hamilton at the Fountain of Youth Stadium when the Light Blues equalled a Scottish clean sheet record set in 1906, having started 2020/21 with six in a row in the Premiership.
He said: "We are very happy about that and the start of the season is going very well.
"I think the performance [against Hamilton] was very good. We kept a clean sheet and I think the only thing we can improve is in the last third and that we can score more goals because I think we create enough chances.
Barisic continues to be an attacking threat week in week out for the Gers, with his powerful runs and accurate crossing making him a standout performer.
The 27-year-old left-back believes the way the team is playing is helping him get forward into advanced positions.
He added: "We change a little bit some of the things, I stay very high and wide as you can see. So, of course, when I'm there and when I'm closer to the goal it is easier for me.
"But I always said if the team is playing very well and if we have the ball and keep the ball more chances will come to try to assist or score the goals. It is just part of the very good team play."