Glasgow Warriors have been drawn in the same group as Montpellier, Bath and Toulouse in next season's inaugural European Rugby Champions Cup.
"It's going to be a very tough pool for us," said head coach Gregor Townsend.
"It will depend on who's on form but the good news for me is that I know my team will get better for the experience of playing these sides."
In the European Challenge Cup, Edinburgh are in Pool 4 along with Bordeaux-Begles, London Welsh and Lyon.
The draws for the new tournaments, replacements for the Heineken Cup and Amlin Challenge Cup, took place in Neuchatel, Switzerland, with five pools of four teams in each cup.
The five pool winners and three best runners-up will secure quarter-final places.
Match dates have yet to be announced.
Warriors, who lost to Leinster in the final of this season's Rabo Pro12, were in the top tier of seeds in Pool 4, which meant they could not be in the same pool as the Dublin side or Toulon, Saracens or Northampton Saints.
That, though, did not prevent them from facing tough opposition.
Toulouse are the fourth seeds in the pool, yet they have won the Heineken Cup four times and last season finished fourth in France's Top 14.
And Townsend will no doubt be wary of Montpellier, a team he played for a decade ago, as they finished second last term in France's top league.
Bath, one of seven top-tier English sides in the Champions Cup, finished fifth in Aviva Premiership.
"To go away twice to France, we will need to play really well and we will learn a lot in those games," Townsend told BBC Scotland.
"We want to improve every season and in Europe we only managed two wins last season and we know we didn't play as well as expected.
"It will be tougher this time, so we'll need to play much better. To get out of your pool, you must play well in every game, especially the ones at home."
Edinburgh will also face two French teams when they compete in the European Rugby Challenge Cup.
They will play Bordeaux-Begles, eighth in the Top 14 in the season just ended, and Lyon, who won the second-tier league in France last season, plus London Welsh.
"I think Lyon are going to provide the strongest opposition - they have just been promoted into the Top 14 and are going well," head coach Alan Solomons told his club website.
Full draw for the 2014/15 European Rugby Champions Cup:
Pool 1: Saracens, Munster, Clermont Auvergne, Sale Sharks
Pool 2: Leinster, Castres, Harlequins, London Wasps
Pool 3: Toulon, Leicester Tigers, Ulster, Scarlets
Pool 4: Glasgow Warriors, Montpellier, Bath, Toulouse
Pool 5: Northampton Saints, Racing Metro, Ospreys, Benetton Treviso.
Full draw for the 2014/15 European Rugby Challenge Cup:
Pool 1: Cardiff Blues, London Irish, Grenoble, FIRA 1 qualifier.
Pool 2: Exeter, Bayonne, Connacht, La Rochelle.
Pool 3: Stade Francais, Newport Gwent Dragons, Newcastle, FIRA 2 qualifier.
Pool 4: Edinburgh, Bordeaux-Begles, London Welsh, Lyon.
Pool 5: Gloucester, Brive, Zebre, Oyonnax.