FAIRFIELD — The town is asking a federal court to make Time Warner Cable Northeast pay $353,000 in unpaid franchise fees, while the cable company has filed its own motion, calling Fairfield’s claims baseless.

In a motion for summary judgment filed Wednesday in U.S. District Court in Bangor, the town says the company has not paid the 5 percent of the gross revenue it collected in town, as required by a 2005 agreement.

The town filed a lawsuit against Time Warner in October to recoup the unpaid fees. A municipality can arrange for a cable company to pay a franchise fee to the local government in exchange for using the town’s infrastructure. The cable company can pass those fees through to consumers as part of their cable bill.

According to the town, Time Warner was paying it 5 percent of only the revenue it collected for basic cable services, not its gross revenue from the town. The difference between the two amounts was $55,000 to $60,000 per year since 2009, for a total of $352,981.

“Much of the matter involves interpretation of the contract language,” said Bill Lee, Fairfield’s town attorney.

But Time Warner, in its own motion filed on Wednesday, said the town misinterpreted the franchise agreement and was unauthorized to increase the fees “unilaterally” to 5 percent of the gross.

“Time Warner Cable’s franchise agreement with the town makes it clear franchise fees are to be collected and paid on revenue from limited TV service only,” company spokeswoman Nathalie Burgos said in an email Thursday, “and our annual filings with the town show we have collected and paid franchise fees appropriately.”

In 2005, the Town Council authorized then-Town Manger Paul Blanchette to request that Adelphia, then the cable provider in town, increase its franchise fee from 3 percent of the gross revenue from basic cable service to 5 percent of gross revenue, as it believed it was entitled to under the franchise agreement.

Blanchette wrote a request to the company, outlining the council’s request. Blanchette died in 2010.

According to the town, the issue didn’t come up again until last year, when Town Manager Josh Reny obtained a copy of Blanchette’s letter and determined that Time Warner, which bought Adelphia, had been paying the town 5 percent of gross revenue only from basic cable, setting off the dispute, Lee said Thursday.

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