* Fujifilm soars on Ebola treatment hope * Market focused on the pace of U.S. rate rise * Exporters strong on weaker yen By Ayai Tomisawa TOKYO, Oct 6 (Reuters) - Japan's Nikkei share average rose on Monday morning after a stronger-than-expected September U.S. jobs report bolstered sentiment, while Fujifilm Holdings Corp soared on hopes that its influenza drug may cure Ebola.

The Nikkei share average rose 1.3 percent to 15,911.44 after gaining 0.3 percent on Friday.

The Labor Department reported that U.S. nonfarm payrolls rose by 248,000 last month and the jobless rate fell two-tenths of a point to 5.9 percent.

"The market is optimistic about the U.S. economy. The next thing the market watches is how fast U.S. rates will rise," said Masashi Oda, chief investment officer at Sumitomo Mitsui Trust Bank. "Higher rates are good, but if the rates rise too fast, the stock market will likely get hit." Fujifilm rose 5.1 percent to a six-year high of 3,580 yen and was the third most traded stock by turnover after a volunteer nurse who was the first French national to contract Ebola left hospital after being successfully treated.

Japan's Fujifilm Holdings said in a statement last month that its Avigan treatment had been administered to the French Ebola patient.

"I've made a chunk of money by investing in Fujifilm last week," said a fund manager at a Japanese asset management. "It's one of the top picks in our portfolio." Exporters were steady as the dollar was up about 0.1 percent in early trading at 109.82 yen, moving back toward last week's six-year peak of 110.09 yen.

Toyota Motor Corp rose 1.7 percent, Honda Motor Co gained 2.6 percent and Panasonic Corp 2.0 percent.

The broader Topix advanced 1.3 percent to 1,299.19, and the JPX-Nikkei Index 400 added 1.3 percent to 11,810.89.

(Editing by Richard Borsuk)