No, you pay a 0% capital gains rate for income that falls under the 15% earned income tax bracket. The capital gains count as income though, so only the gains that fall under that income limit after accounting for your regular income.
BUT, there is an exclusion for the first $250k single / $500k married of gains from the sale of real estate that was your primary residence for at least 2 of the last 5 years. I'm not sure how this would interact with the 0% capital gains rate for gains above that.
Do you have records of what you've paid for repairs and improvements on the home over the years? Those would help reduce the gains.