PARIS (Reuters) - Vivendi has reached an agreement to buy out partner Lagardere's 20 percent stake in pay-television operator Canal+ France for 1.02 billion euros ($1.41 billion), the companies said on Monday.

The accord puts an end to a long-running battle between the two French media groups, having finally met halfway on price after legal mediation that began in May.

Lagardere valued its stake in Canal+ France at 1.15 billion euros in its accounts, while Vivendi believed it was worth 800-900 million euros, a source familiar with the situation told Reuters.

"This agreement, which will be submitted for information to the appropriate works councils, puts an end to all disputes between the two groups related to this participation," the companies said in a joint statement.

Canal+ France is a unit of Canal+, Vivendi's international pay-TV business, which is smaller than British peer BSkyB and News Corp-owned pay-TV operators in Europe.

For Vivendi, the deal rids it of a minority shareholder in Canal+ at a time when pay-TV is set to become a bigger priority. Vivendi is in the midst of a restructuring to pay down debt, shed telecoms assets in Morocco and elsewhere and focus on its TV and music businesses.

Canal+ contributed roughly a quarter of Vivendi's sales of 10.84 billion euros in the first half of the year. Those figures are restated to reflect Vivendi's sale of Maroc Telecom and video games maker Activision Blizzard.

Vivendi and Lagardere have been in court since February, when Lagardere sued Vivendi for 1.6 billion euros in damages over Canal+. It argued that Vivendi made permanent use of the business's entire cash surplus under a disputed cash management agreement between the venture and its parent company.

They began arbitration in May, which was extended by several weeks in early October to try to reach an accord.

UBS analyst Polo Tang, who valued Lagardere's Canal+ France stake at 800 million euros, said before the accord was announced that it would be good for Lagardere shareholders because it could lead to further cash returns.

Tang added that Canal+ was a low-growth asset that had been hurt by competition from subscription sports channel BeIn Sport, which is backed by Gulf TV broadcaster Al Jazeera.

The acquisition would also reduce shareholder returns for Vivendi from the previously expected 4 billion euros to 3 billion euros, UBS said.

Vivendi has not yet indicated how much of the proceeds of the Maroc Telecom and Activision sales it will return to shareholders. ($1 = 0.7254 euros)

(Reporting by Lionel Laurent and Leila Abboud; Editing by Natalie Huet and David Goodman)