if rmse is high then R2 may be low and F statistics may yield p-value greater then 0.05. so please shareoutput. because these all depend on sum of squares of residuals. but if in your case rmse is high F-stat has low p-value , all the coefficients are significant, there is no auto in the residuals then model can be said as good. (keeping in mind before fitting a model that there is no structural break and/or outliers in the series)
your model obviously contains some sort of misspecification. This misspecification can be theoretically trivial and concern unimportant aspects (if there are any) or fundamental. If the RMSEA is "too high", the chi-square test will be significant, too (which should guide the evalution). To get a hint where the problem may lie you have to consider any information that could be helpful (standardized residuals, implausible estimates) in addition to learn/understand what a CFA/SEM really does (the keywords are d-separation and path tracing rules).
RMSEA indicates the badness of fit. This normally occur due to wrong model specification. Redundancy among items and redundancy among the constructs could also contribute to poor RMSEA.