This is The Helping Hand (19911) by Norman Spinrad.
A summary (emphasis mine, spelling fixed):
In “The Helping Hand” by Norman Spinrad, NASA received a radio signal from a planet orbiting Barnard’s star, proving there might be other life. Soon they decode the transmissions and release them to the public. Images of creatures in need of help appear. The humans work together and raise enough money to go on a long journey to Barnard’s star to save these creatures. But when they get there, it turns out that it was an elaborate plan to make the Earth a better place. To save the Barnards, the humans put their differences aside and it brought out the best in them.
From this site
A quote (emphasis mine, spelling fixed):
The Earth has sent a starship called the Helping Hand to save the Barnard's star. It began with 200 men and women from all different countries.
Passage via this site
It was published in Full Spectrum 3 (1991, English), Galaxies #39 (2006, French), and Utopiales 2013 (2013, French)2.
Found this by looking at John Rennie's answer to another question.
2Called "La main tendue" in French.