This was a bizarre competition involving clubs from France, England and Scotland and modelled on the Franco-Italian Friendship tournament http://www.rsssf.com/tablesf/francoitalian.html
for more details
Celtic and Clyde, as you say, took part in the first competition as did Motherwell and Dundee. Participation was based on league position. The top three in 1959-60 (Hearts, Kilmarnock, Rangers) were entered for the European Cup, New York International tournament and Cup-Winners Cup and 7th-placed Hibs in the Fairs cup so places should have gone to 4th,5th, 6th and 8th (Dundee, Motherwell, Clyde, Ayr United) but as Ayr had no floodlights, 9th-placed Celtic made up the numbers.
The first legs were played in early August a week before the start of the Scottish season. Celtic were beaten 3-0 by Sedan and Dundee lost 1-0 against Valenciennes. It was hardly a popular tournament with just 3,000 at the Celtic match and 2,000 for Dundee’s game.
Attendances were better for the Scottish legs with 27,000 at Celtic Park to see a 3-3 draw and 7,000 for Dundee’s 4-2 home win. The Parkhead match was on October 18th and the Dens Park return not until December 7th.
Clyde and Motherwell won both home and away against Lens and Toulouse respectively to give the Scottish clubs eleven points to the French clubs five.
Based on league positions the participants the next season would have been the clubs finishing 3rd-6th in 1960-61(Third Lanark, Celtic, Motherwell and Aberdeen) but quite what happened I’m not sure. Third Lanark played and lost twice to Rouen, 2-1 on both occasions. Celtic didn’t take part as they couldn’t agree dates with opponents Reims.
I don’t know what happened to Motherwell and Aberdeen.
if anyone has any further information for Terry, including English sides, please add below