In an anthology that I read in high school (1980s), there was a short story which had a feline alien race that was cooperating with humans from a wrecked starship. It took at least one human generation to fix the ship. The aliens were faster, more dexterous, and more agile than humans, but had only Iron Age technology. The city of the humans' allies was being invaded and many of the humans were conflicted because they were getting ready to leave finally, having had several of their children go native. If it helps, I believe that there was an excerpt from the Lensman series by EE Doc Smith in the same volume.
I'm pretty sure you read Poul Anderson's novelette "Star Ship" in the 1974 anthology Space Odysseys edited by Brian Aldiss. For one thing (as you can see from the table of contents), this anthology does contain an extract from Doc Smith's Galactic Patrol.
The story matches your description in most respects. Spacewrecked humans need help from felinoid natives with Iron Age tech to get back into space; the project takes a human generation; the children are going native, the natives are restless. The big discrepancy is that they are not trying to fix a wrecked starship. The starship is in orbit, unharmed, unattended, unreachable. All the people on the starship (yes, they admitted afterward that it was pretty foolish) rode the shuttlecraft down to a crash landing on the planet. There is no hope of repairing the shuttlecraft or replicating its "gravity drive" with Iron Age technology. The plan is to build a chemical rocket ship capable of making a rendezvous with the orbiting starship.
Besides, the Terrestrials had had to learn much from scratch themselves. None of them had ever built a rocket ship, had ever seen one in action even. It was centuries obsolete in Galactic civilization. So--they'd had to design the ship from the ground up. Which meant years of painstaking research . . . and only a few interested humans and Khazaki to do it. The rest were too busy with their brawling, barbaric culture.
CJ Cherryh wrote at least three books about a felineoid race called the Chanur. One question, if your characters had only iron-age technology, how did they get a spaceship?
Sounds a lot like Vernor Vinge A fire upon the deep, except that's a novel instead of a short story and aliens are more wolf like than feline.